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  • Engineering General  (1.423)
  • D90
  • 2020-2020
  • 1995-1999  (1.432)
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  • 1
    Digitale Medien
    Digitale Medien
    Consumption choice and asset pricing with a non-price-taking agent (1997)
    Springer
    Economic theory 10 (1997), S. 437-462 
    Details
    ISSN: 1432-0479
    Schlagwort(e): JEL Classification Numbers: C60 ; D42 ; D51 ; D90 ; G12.
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Summary. This paper develops a pure-exchange model to study the consumption-portfolio problem of an agent who acts as a non-price-taker, and to analyze the implications of his behavior on equilibrium security prices. The non-price-taker is modeled as a price leader in all markets; his price impact is then recast as a dependence of the Arrow-Debreu prices on his consumption, allowing a tractable formulation. Besides the aggregate consumption, the endowment of the non-price-taker appears as an additional factor in driving equilibrium allocations and prices. Comparisons of equilibria between a price-taking and a non-price-taking economy are carried out.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s001990050166
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  • 2
    Digitale Medien
    Digitale Medien
    Optimal growth and cycles in overlapping generations models (1997)
    Springer
    Economic theory 9 (1997), S. 511-528 
    Details
    ISSN: 1432-0479
    Schlagwort(e): D90
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Summary This paper investigates the dynamical properties of optimal paths in one-sector overlapping generations models without assuming that the utility function of the representative agent is separable. When the utility function is separable, the optimal growth paths monotonically converges toward the modified golden rule steady state. In the non-separable case, we show that the optimal growth path may be oscillating and optimal two-period cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogeneous fluctuations provided that the discount factor is close enough to one. All our results are illustrated using Cobb-Douglas utility and production functions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01213852
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  • 3
    Digitale Medien
    Digitale Medien
    Optimal accumulation in a small open economy with technological uncertainty (1999)
    Springer
    Economic theory 13 (1999), S. 207-219 
    Details
    ISSN: 1432-0479
    Schlagwort(e): JEL Classification Numbers: C61 ; D90 ; O41.
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Summary. This paper analyzes the optimal allocation problem of a small trading country facing an uncertain technology. It is involved in production of many commodities. Differentiability cannot be guaranteed, hence, the Ramsey-Euler condition of optimality needs to be modified. From the optimality criterion, we derive a pair of conditions, which does not require differentiability. If “enough” uncertainty is allowed, the sequence of the distribution functions of investment expenditure converges uniformly to a unique invariant measure. In addition to the weak convergence of the stochastic process of investment expenditure we also have the sequences of the stochastic process of investment expenditure converging weakly.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s001990050249
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  • 4
    Digitale Medien
    Digitale Medien
    Consistent planning, backwards induction, and rule-governed behavior (1996)
    Springer
    Constitutional political economy 7 (1996), S. 35-48 
    Details
    ISSN: 1572-9966
    Schlagwort(e): A12 ; D10 ; D90
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Abstract This paper argues that with regard to sequential choice problems the set of assumptions that are necessary for the process of planning to be logically consistent may make the notion of rational dynamic consistency an unacceptable prescription for choice. In this sense, motivational limits to rationality may arise, adding to the inability of making consistent plans an unwillingness to engage in planning consistently. A different notion of planning, centered around the notion of self-commitment and rule-governed behavior may appear to be a more natural solution to optimal sequential choice.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00143478
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  • 5
    Digitale Medien
    Digitale Medien
    Eliciting individual discount rates (1999)
    Springer
    Experimental economics 2 (1999), S. 107-127 
    Details
    ISSN: 1573-6938
    Schlagwort(e): experimental economics ; discount rates ; censored dependent variable ; C91 ; D90
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Abstract Controlled laboratory conditions using monetary incentives have been utilized in previous studies that examine individual discount rates, and researchers have found several apparently robust anomalies. We conjecture that subject behavior in these experiments may be affected by (uncontrolled) factors other than discount rates. We address some experimental design issues and report a new series of experiments designed to elicit individual discount rates. Our primary treatments include: (i) informing subjects of the annual and effective interest rates associated with alternative payment streams, and (ii) informing subjects of current market interest rates. We also test for the effect of real (vs. hypothetical) payments and for the effect of delaying both payment options (vs. offering an immediate payment option). The statistical analysis uses censored data techniques to account for the interactions between field and lab incentives. Each of the information treatments appears to reduce revealed discount rates. When both types of information are provided, annual rates in the interval of 15%–17.5% are revealed, whereas rates of 20%–25% are revealed in the control session. Each of the treatments also lowers the residual variance of subject responses.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01673482
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  • 6
    Digitale Medien
    Digitale Medien
    Redistribution and growth: Pareto improvements (1996)
    Springer
    Journal of economic growth 1 (1996), S. 505-523 
    Details
    ISSN: 1573-7020
    Schlagwort(e): Endogenous growth ; redistribution ; wealth distribution ; D31 ; D90 ; O30 ; O41
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Abstract This paper analyzes the relationship between income distribution and economic growth. It introduces heterogeneous households who have preferences for leisure into Grossman and Helpman's model of endogenous growth (in which income distribution has no effect on economic growth). Wealth distribution affects the endogenous rate of growth as the labor supply of each individual responds inversely to his permanent income. When the labor Engel curve is concave (convex), unequal wealth distribution decreases (increases) the rate of growth. Pareto-improving-growth-enhancing wealth redistributions are characterized.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00150199
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  • 7
    Digitale Medien
    Digitale Medien
    Rationalizable expectations and sunspot equilibria in an overlapping-generations economy (1997)
    Springer
    Journal of economics 65 (1997), S. 257-277 
    Details
    ISSN: 1617-7134
    Schlagwort(e): market uncertainty ; overlapping generations ; rational expectations ; rationalizable expectations ; sunspots ; D51 ; D84 ; D90 ; E21
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Abstract There are two theories for the treatment of market uncertainty: rationalizable expectations and sunspot equilibria. This paper shows how the game-theoretic solution concept of rationalizable expectations can be applied to an overlapping-generations exchange economy. Some general properties of these equilibria are discussed. It is shown that rationalizable-expectations equilibria are the predictions yielded by considering sunspot equilibria in which probability beliefs may differ across individuals. This result allows for a new interpretation of sunspot equilibria and helps to understand their relevance.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01226845
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  • 8
    Digitale Medien
    Digitale Medien
    Infinite-horizon competitive programs are optimal (1999)
    Springer
    Journal of economics 69 (1999), S. 217-238 
    Details
    ISSN: 1617-7134
    Schlagwort(e): optimal programs ; competitive conditions ; transversality condition ; intertemporal decentralization ; C61 ; D90 ; O41
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Abstract For infinite-horizon optimal-growth problems the standard result in the literature says that a program is optimal if and only if associated with it is a sequence of present-value prices at which the program satisfies (i) a set of myopic “competitive conditions,” and (ii) an asymptotic “transversality condition”. The principal result of this paper points out the interesting and surprising fact that at least for a class of multisector models where the production side is described by a simple linear model, and there are some limiting primary factors, the competitive conditions alone characterize an optimal program.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01231160
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  • 9
    Digitale Medien
    Digitale Medien
    On the equivalence between the overlapping-generations model and cyclical general-equilibrium models (1999)
    Springer
    Journal of economics 70 (1999), S. 187-207 
    Details
    ISSN: 1617-7134
    Schlagwort(e): overlapping generations ; general equilibrium ; cycles ; D51 ; D90 ; E32
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Wirtschaftswissenschaften
    Notizen: Abstract We show that equilibrium cycles in an overlapping-generations model are equivalent to asymmetric equilibria in a general-equilibrium model. We use this equivalence to find equilibrium cycles in the overlapping-generations model with two and three generations, respectively. For the example with two generations we show that for certain parameter values cycles of all periods occur.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01224768
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  • 10
    Digitale Medien
    Digitale Medien
    A modified direct preconditioner for indefinite symmetric Toeplitz systems (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 415-429 
    Details
    ISSN: 1070-5325
    Schlagwort(e): indefinite ; inverse ; preconditioning ; symmetric ; Toeplitz ; Trench algorithm ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A modification is presented of the classical O(n2) algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm is stable for symmetric matrices that are positive definite, but can be unstable for the indefinite case (and for general matrices). Our modification permits extension of the algorithm to compute approximate inverses of indefinite symmetric Toeplitz matrices, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, the approximate inverse has an advantage that only matrix - vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover, that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.
    Zusätzliches Material: 1 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020504
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  • 11
    Digitale Medien
    Digitale Medien
    Conference diary (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 483-485 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020509
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  • 12
    Digitale Medien
    Digitale Medien
    Completely parallelizable preconditioning methods (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 447-465 
    Details
    ISSN: 1070-5325
    Schlagwort(e): preconditioned iterative methods ; SSOR factorization ; parallelization ; connection machine ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A class of parallelizable preconditioned iterative methods for the solution of certain finite difference or finite element linear systems of equations is presented. The methods are based on calculation of approximate inverses of the SSOR factorization. The speed of the methods may be increased by making the approximation of the inverse more accurate. The construction of the preconditioning as well as the solution of the preconditioning systems (realized by matrix-vector multiplication) can be made in parallel over the total amount of meshpoints. The methods are suitable for implementation on massively parallel computers such as connection machines. Problems with constant as well as strongly varying orthotropy are examined and the methods are compared to other parallel techniques with respect to rate of convergence, computational complexity and consumed CM200 computing time. We report a small but significant decrease in computing time compared to the (until now) most frequently used completely parallel preconditioning, the Jacobi method.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020506
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  • 13
    Digitale Medien
    Digitale Medien
    A saxpy formulation for plane rotations (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 533-541 
    Details
    ISSN: 1070-5325
    Schlagwort(e): plane rotation ; shear product ; Saxpy operation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An algorithm for pre- or post-multiplication of a matrix by a plane rotation, using only three vector saxpy operations instead of the four vector operations usually considered necessary, is described. No auxiliary storage for overwriting is required. The method is shown to be numerically stable.
    Zusätzliches Material: 6 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020605
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  • 14
    Digitale Medien
    Digitale Medien
    Multilevel preconditioners for discretizations of the biharmonic equation by rectangular finite elements (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 487-505 
    Details
    ISSN: 1070-5325
    Schlagwort(e): biharmonic equation ; rectangular finite elements ; preconditioning ; multilevel methods ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Recently, some new multilevel preconditioners for solving elliptic finite element discretizations by iterative methods have been proposed. They are based on appropriate splittings of the finite element spaces under consideration, and may be analyzed within the framework of additive Schwarz schemes. In this paper we discuss some multilevel methods for discretizations of the fourth-order biharmonic problem by rectangular elements and derive optimal estimates for the condition numbers of the preconditioned linear systems. For the Bogner-Fox-Schmit rectangle, the generalization of the Bramble-Pasciak-Xu method is discussed. As a byproduct, an optimal multilevel preconditioner for nonconforming discretizations by Adini elements is also derived.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020603
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  • 15
    Digitale Medien
    Digitale Medien
    Preconditioning Mixed Finite Element Saddle-point Elliptic Problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 1-20 
    Details
    ISSN: 1070-5325
    Schlagwort(e): preconditioning saddle-point problems ; eigenvalue estimation ; mixed finite element method ; minimum residual method ; second-order elliptic problems ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider saddle-point problems that typically arise from the mixed finite element discretization of second-order elliptic problems. By proper equivalent algebraic operations the considered saddle-point problem is transformed to another saddle-point problem. The resulting problem can then be efficiently preconditioned by a block-diagonal matrix or by a factored block-matrix (the blocks correspond to the velocity and pressure, respectively). Both preconditioners have a block on the main diagonal that corresponds to the bilinear form(δ is a positive parameter) and a second block that is equal to a constant times the identity operator. We derive uniform bounds for the negative and positive eigenvalues of the preconditioned operator. Then any known preconditioner for the above bilinear form can be applied. We also show some numerical experiments that illustrate the convergence properties of the proposed technique.
    Zusätzliches Material: 2 Tab.
    Materialart: Digitale Medien
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  • 16
    Digitale Medien
    Digitale Medien
    Masthead (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030101
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  • 17
    Digitale Medien
    Digitale Medien
    Multifrontal QR Factorization in a Multiprocessor Environment (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 275-300 
    Details
    ISSN: 1070-5325
    Schlagwort(e): sparse QR factorization ; multifrontal method ; parallelism ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We describe the design and implementation of a parallel QR decomposition algorithm for a large sparse matrix A. The algorithm is based on the multifrontal approach and makes use of Householder transformations. The tasks are distributed among processors according to an assembly tree which is built from the symbolic factorization of the matrix ATA.We first address uniprocessor issues and then discuss the multiprocessor implementation of the method. We consider the parallelization of both the factorization phase and the solve phase. We use relaxation of the sparsity structure of both the original matrix and the frontal matrices to improve the performance. We show that, in this case, the use of Level 3 BLAS can lead to very significant gains in performance. We use the eight processor Alliant˜FX/80 at CERFACS to illustrate our discussion.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
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  • 18
    Digitale Medien
    Digitale Medien
    Two-stage Multisplitting Methods with Overlapping Blocks (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 113-124 
    Details
    ISSN: 1070-5325
    Schlagwort(e): iterative methods ; linear systems ; multisplittings ; overlap ; parallel algorithms ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Parallel two-stage multisplitting methods with overlap for the solution of linear systems of algebraic equations are studied. It is shown that, under certain hypotheses, the method with overlap is asymptotically faster than that without overlap. Experiments illustrating this phenomenon are presented.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 19
    Digitale Medien
    Digitale Medien
    On Fast Computations with the Inverse to Harmonic Potential Operators via Domain Decomposition (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 91-111 
    Details
    ISSN: 1070-5325
    Schlagwort(e): boundary integral operators ; domain decomposition ; interface operators ; fast elliptic problem solvers ; parallel algorithms ; preconditioning ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper a method for fast computations with the inverse to weakly singular, hypersingular and double layer potential boundary integral operators associated with the Laplacian on Lipschitz domains is proposed and analyzed. It is based on the representation formulae suggested for above-mentioned boundary operations in terms of the Poincare-Steklov interface mappings generated by the special decompositions of the interior and exterior domains. Computations with the discrete counterparts of these formulae can be efficiently performed by iterative substructuring algorithms provided some asymptotically optimal techniques for treatment of interface operators on subdomain boundaries. For both two- and three-dimensional cases the computation cost and memory needs are of the order O(N logp N) and O(N log2 N), respectively, with 1 ≤ p ≤ 3, where N is the number of degrees of freedom on the boundary under consideration (some kinds of polygons and polyhedra). The proposed algorithms are well suited for serial and parallel computations.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 20
    Digitale Medien
    Digitale Medien
    Short Communication: Two Properties of Diagonally Dominant Matrices (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 173-177 
    Details
    ISSN: 1070-5325
    Schlagwort(e): diagonally dominant matrix ; determinant ; norm ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A property of strictly diagonally dominant matrices and a generalization of a Varga's bound for ∥ A-1∥∞ to the case ∥ A-1B∥∞ are given and the two-sided bounds for the determinants of strictly diagonally dominant matrices are derived
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  • 21
    Digitale Medien
    Digitale Medien
    Piecewise Polynomial Solutions Without a priori Break Points (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 513-524 
    Details
    ISSN: 1070-5325
    Schlagwort(e): regularization ; I-norm ; discontinuous solutions ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In certain inverse problems it is useful to be able to compute solutions which are, in some sense, as simple as possible. For example,k one may wish to compute solutions which are piecewise constant and with as few discontinuities as possible. Such solutions are suited to describe models, e.g., geological layers, where the coarse structure is more important than the fine structure. A natural generalization of piecewise constant functions is piecewise polynomial solutions. In this paper we present a new algorithm which is capable of computing solutions that are piecewise polynomials, without having to specify a priori the positions of the break points between the polynomial pieces.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 22
    Digitale Medien
    Digitale Medien
    On IOM(q): The Incomplete Orthogonalization Method for Large Unsymmetric Linear Systems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 491-512 
    Details
    ISSN: 1070-5325
    Schlagwort(e): unsymmetric ; Krylov subspace ; IOM(q) ; FOM ; truncated ; basis vector ; orthonormality ; convergence ; restarted ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The incomplete orthogonalization method (IOM(q)), a truncated version of the full orthogonalization method (FOM) proposed by Saad, has been used for solving large unsymmetric linear systems. However, no convergence analysis has been given. In this paper, IOM(q) is analysed in detail from a theoretical point of view. A number of important results are derived showing how the departure of the matrix A from symmetric affects the basis vectors generated by IOM(q), and some relationships between the residuals for IOM(q) and FOM are established. The results show that IOM(q) behaves much like FOM once the basis vectors generated by it are well conditioned. However, it is proved that IOM(q) may generate an ill-conditioned basis for a general unsymmetric matrix such that IOM(q) may fail to converge or at least cannot behave like FOM. Owing to the mathematical equivalence between IOM(q) and the truncated ORTHORES(q) developed by Young and Jea, insights are given into the convergence of the latter. A possible strategy is proposed for choosing the parameter q involved in IOM(q). Numerical experiments are reported to show convergence behaviour of IOM(q) and of its restarted version.
    Zusätzliches Material: 6 Tab.
    Materialart: Digitale Medien
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  • 23
    Digitale Medien
    Digitale Medien
    Matrix shapes invariant under the symmetric QR algorithm (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 87-93 
    Details
    ISSN: 1070-5325
    Schlagwort(e): QR algorithm ; zero pattern ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The QR algorithm is a basic algorithm for computing the eigenvalues of dense matrices. For efficiency reasons it is prerequisite that the algorithm is applied only after the original matrix has been reduced to a matrix of a particular shape, most notably Hessenberg and tridiagonal, which is preserved during the iterative process. In certain circumstances a reduction to another matrix shape may be advantageous. In this paper, we identify which zero patterns of symmetric matrices are preserved under the QR algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020203
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  • 24
    Digitale Medien
    Digitale Medien
    Efficient reduction algorithms for bordered band matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 95-113 
    Details
    ISSN: 1070-5325
    Schlagwort(e): arrowhead matrix ; band matrix ; inverse eigenvalue problem ; givens rotations ; singular value decomposition ; updating ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Various plane rotation patterns are presented, which provide stable algorithms for reducing a b-band matrix bordered by p rows and/or columns to (b + p)-band form. These schemes generalize previously presented O(N2) reduction algorithms for matrices of order N, b = 1, and p = 1 to the reduction of more general b-band, p-bordered matrices where b ≥ 1 and p ≥ 1. Moreover, by splitting the matrix into two similarly structured submatrices and chasing nonzeros to the corners in two directions, the newly proposed patterns reduce the number of required rotations and hence the computational cost by one half compared to the other existing one-way chasing algorithms. Symmetric, as well as more general matrices, are considered. An example of the first type is the symmetric arrowhead matrix that arises in solving inverse eigenvalue problems. Examples of the second type are found in updating the singular value decomposition (SVD) and the partial SVD.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020204
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  • 25
    Digitale Medien
    Digitale Medien
    Block Two-stage Methods for Singular Systems and Markov Chains (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 413-426 
    Details
    ISSN: 1070-5325
    Schlagwort(e): iterative methods ; linear systems ; singular matrices ; block methods ; multisplitting ; two-stage ; non-stationary ; Markov chains ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The use of block two-stage methods for the iterative solution of consistent singular linear systems is studied. In these methods, suitable for parallel computations, different blocks, i.e., smaller linear systems, can be solved concurrently by different processors. Each of these smaller systems are solved by an (inner) iterative method. Hypotheses are provided for the convergence of non-stationary methods, i.e., when the number of inner iterations may vary from block to block and from one outer iteration to another. It is shown that the iteration matrix corresponding to one step of the block method is convergent, i.e., that its powers converge to a limit matrix. A theorem on the convergence of the infinite product of matrices with the same eigenspace corresponding to the eigenvalue 1 is proved, and later used as a tool in the convergence analysis of the block method. The methods studied can be used to solve any consistent singular system, including discretizations of certain differential equations. They can also be used to find stationary probability distribution of Markov chains. This last application is considered in detail.
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  • 26
    Digitale Medien
    Digitale Medien
    Editorial (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 349-350 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: No Abstract
    Materialart: Digitale Medien
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  • 27
    Digitale Medien
    Digitale Medien
    Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 427-453 
    Details
    ISSN: 1070-5325
    Schlagwort(e): mixed method ; nonconforming method ; multilevel preconditioner ; condition number ; second order elliptic problem ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A new approach for constructing algebraic multilevel preconditioners for mixed finite element methods for second order elliptic problems with tensor coefficients on general geometry is proposed. The linear system arising from the mixed methods is first algebraically condensed to a symmetric, positive definite system for Lagrange multipliers, which corresponds to a linear system generated by standard nonconforming finite element methods. Algebraic multilevel preconditioners for this system are then constructed based on a triangulation of the domain into tetrahedral substructures. Explicit estimates of condition numbers and simple computational schemes are established for the constructed preconditioners. Finally, numerical results for the mixed finite element methods are presented to illustrate the present theory.
    Zusätzliches Material: 4 Ill.
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  • 28
    Digitale Medien
    Digitale Medien
    Conference diary (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 455-457 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030502
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  • 29
    Digitale Medien
    Digitale Medien
    A Comparison of Three Basic Conjugate Direction Methods (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 473-489 
    Details
    ISSN: 1070-5325
    Schlagwort(e): conjugate gradients ; biconjugate gradients ; conjugate directions ; non-symmetric linear systems ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper three basic conjugate direction methods for solving non-symmetric linear systems are described and compared. All three have entirely different basic structures and, consequently, completely different characteristics. The motivation for this work is the comparative assessment of the methods in order to decide which of the three is the most suitable for further development.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
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  • 30
    Digitale Medien
    Digitale Medien
    Masthead (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030601
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  • 31
    Digitale Medien
    Digitale Medien
    Conference diary (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 543-545 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030602
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  • 32
    Digitale Medien
    Digitale Medien
    On Parlett's matrix norm inequality for the Cholesky decomposition (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 243-250 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Cholesky ; norm inequality ; perturbation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We show that a certain matrix norm ratio studied by Parlett has a supermum that is O(\documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[\sqrt n \] $\end{document}) when the chosen norm is the Frobenius norm, while it is O(log n) for the 2-norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n matrix.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020306
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  • 33
    Digitale Medien
    Digitale Medien
    Optimal backward perturbation bounds for the linear least squares problem (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 271-286 
    Details
    ISSN: 1070-5325
    Schlagwort(e): linear least squares ; backward perturbations ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Let A be an m × n matrix, b be an m-vector, and x̃ be a purported solution to the problem of minimizing ‖b  -  Ax‖2. We consider the following open problem: find the smallest perturbation E of A such that the vector x̃ exactly minimizes ‖b  -  (A+E)x‖2. This problem is completely solved when E is measured in the Frobenius norm. When using the spectral norm of E, upper and lower bounds are given, and the optimum is found under certain conditions.
    Zusätzliches Material: 1 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020308
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  • 34
    Digitale Medien
    Digitale Medien
    On the solution of block Hessenberg systems (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 287-296 
    Details
    ISSN: 1070-5325
    Schlagwort(e): block Hessenberg matrix ; block Toeplitz matrix ; linear system ; queue ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper describes a divide-and-conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the fast Fourier transform.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020309
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  • 35
    Digitale Medien
    Digitale Medien
    Announcement (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. ii 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020602
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  • 36
    Digitale Medien
    Digitale Medien
    Implicit Cholesky algorithms for singular values and vectors of triangular matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 507-531 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Cholesky decomposition ; singular values ; eigenvalues ; null spaces ; noise spaces ; URV and ULV factorizations ; QR algorithm ; LR algorithm ; Jacobi methods ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The implicit Cholesky algorithm has been developed by several authors during the last 10 years but under different names. We identify the algorithm with a special version of Rutishauser's LR algorithm. Intermediate quantities in the transformation furnish several attractive approximations to the smallest singular value.The paper extols the advantages of using shifts with the algorithm. The nonorthogonal transformations improve accuracy.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020604
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  • 37
    Digitale Medien
    Digitale Medien
    Conference diary (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 543-545 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020606
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  • 38
    Digitale Medien
    Digitale Medien
    Toeplitz Preconditioners with Block Structure for First-order PDEs (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 21-44 
    Details
    ISSN: 1070-5325
    Schlagwort(e): first-order PDEs ; iterative methods ; preconditioners ; Toeplitz ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Preconditioners to nonsymmetric, nondiagonally dominant systems of equations are constructed and examined numerically. The preconditioners are based on a Toeplitz approach with a certain symmetry that we define. The inversion of the preconditioners is defined through a Fast Modified Sine Transform. As a model problem we study the systems of equations arising from a implicit time-discretization with a large time-step of a scalar hyperbolic PDE.
    Zusätzliches Material: 17 Ill.
    Materialart: Digitale Medien
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  • 39
    Digitale Medien
    Digitale Medien
    Generalization of Strang's Preconditioner with Applications to Toeplitz Least Squares Problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 45-64 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Toeplitz least squares problems ; circulant preconditioned conjugate gradient method ; deconvolution ; image restoration ; atmospheric imaging ; medical imaging ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The th column of our circulant preconditioner Sn is equal to the th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix An has decaying coefficients away from the main diagonal, then is a good preconditioner for An. Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min ∥ b - Ax∥2. Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 40
    Digitale Medien
    Digitale Medien
    A Parallel Preconditioned Iterative Realization of the Panel Method in 3D (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 65-80 
    Details
    ISSN: 1070-5325
    Schlagwort(e): boundary value problem ; boundary element method ; preconditioning ; iterative method ; fast Fourier transform ; parallel algorithm ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCube-2 parallel computer showing that preconditioned iterative methods are very well suited also in three-dimensional cases for implementation on an MIMD computer and that they are much more efficient than usual direct solution techniques.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 41
    Digitale Medien
    Digitale Medien
    Conference diary (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 91-93 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030102
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  • 42
    Digitale Medien
    Digitale Medien
    Masthead (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030401
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  • 43
    Digitale Medien
    Digitale Medien
    Conference diary (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 345-348 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030402
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  • 44
    Digitale Medien
    Digitale Medien
    The Finite Difference Based Fast Adaptive Composite Grid Method (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 391-411 
    Details
    ISSN: 1070-5325
    Schlagwort(e): finite difference discretization ; fast adaptive composite grid method ; convergence rate ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The fast adaptive composite grid (FAC) method is an iterative method for solving discrete boundary value problems on composite grids. McCormick introduced the method in [8] and considered the convergence behaviour for discrete problems resulting from finite volume element discretization on composite grids. In this paper we consider discrete problems resulting from finite difference discretization on composite grids. We distinguish between two obvious discretization approaches at the grid points on the interfaces between fine and coarse subgrids. The FAC method for solving such discrete problems is described. In the FAC method several intergrid transfer operators appear. We study how the convergence behaviour depends on these intergrid transfer operators. Based on theoretical insights, (quasi-)optimal intergrid transfer operators are derived. Numerical results illustrate the fast convergence of the FAC method using these intergrid transfer operators.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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  • 45
    Digitale Medien
    Digitale Medien
    Masthead (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030501
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  • 46
    Digitale Medien
    Digitale Medien
    Dykstra's Algorithm for a Constrained Least-squares Matrix Problem (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 459-471 
    Details
    ISSN: 1070-5325
    Schlagwort(e): alternating projection method ; Dykstra's algorithm ; patterned matrix ; constrained least-squares ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We apply Dykstra's alternating projection algorithm to the constrained least-squares matrix problem that arises naturally in statistics and mathematical economics. In particular, we are concerned with the problem of finding the closest symmetric positive definite bounded and patterned matrix, in the Frobenius norm, to a given matrix. In this work, we state the problem as the minimization of a convex function over the intersection of a finite collection of closed and convex sets in the vector space of square matrices.We present iterative schemes that exploit the geometry of the problem, and for which we establish convergence to the unique solution. Finally, we present preliminary numberical results to illustrate the performance of the proposed iterative methods.
    Zusätzliches Material: 4 Tab.
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  • 47
    Digitale Medien
    Digitale Medien
    Analysis of Algorithms for Orthogonalizing Products of Unitary Matrices (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 125-145 
    Details
    ISSN: 1070-5325
    Schlagwort(e): orthogonalization ; QR factorization ; polar decomposition ; subspace tracking ; error analysis ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the problem of computing Uk = QkUk-1(where U0 is given) in finite precision (εM = machine precision) where U0 and theQi are known to be unitary. The problem is that Ûk, the computed product may not be unitary, so one applies an O(n2) orthogonalizing step after each multiplication to(a) prevent Ûk from drifing too far from the set of untary matrices(b) prevent Ûk from drifting too far from Uk the true product.Our main results are1. Scaling the rows to have unit length after each multiplication (the cheaptest of the algorithms considered) is usually as good as any other method with respect to either of the criteria (a) or (b).2. A new orthogonalization algorithm that guarantees the distance of Ûk (k = 1, 2, …) to the set of unitary matrices is bounded by n3.5εM for any choice of Qi.
    Zusätzliches Material: 4 Ill.
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  • 48
    Digitale Medien
    Digitale Medien
    Masthead (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030201
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  • 49
    Digitale Medien
    Digitale Medien
    Estimate of the Constant in Two Strengthened C.B.S. Inequalities for F.E.M. Systems of 2D Elasticity: Application to Multilevel Methods and a Posteriori Error Estimators (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 147-159 
    Details
    ISSN: 1070-5325
    Schlagwort(e): elasticity ; finite-element ; multilevel ; a posteriori error estimation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The constant γ in the strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality plays a crucial role in the convergence rate of multilevel iterative methods as well as in the efficiency of a posteriori error estimators, that is in the framework of finite element approximations of SPD problems.We consider the approximation of the 2D elasticity problem by the Courant element. Concerning multilevel convergence rate, that is the γ corresponding to nested general triangular meshes of size h and 2h, we have proved that γ2≤ 3/4$ uniformly on the mesh and the Poisson ratio. Concerning error estimator, that is the γ corresponding to quadratic and linear approximations on the same mesh, numerical computations have shown that the exact γ for a reference element deteriorates that is goes to one, when the Poisson ratio tends to 1/2
    Zusätzliches Material: 1 Ill.
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  • 50
    Digitale Medien
    Digitale Medien
    On the Smoothing Property of Multigrid Methods in the Non-symmetric Case (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 161-172 
    Details
    ISSN: 1070-5325
    Schlagwort(e): smoothing property ; multigrid method ; semi-iterative smoother ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we present an extension of Reusken's Lemma about the smoothing property of a multigrid method for solving non-symmetric linear systems of equations. One of the consequences of this extended lemma is the verification of the smoothing property for all damping factors οε(0, 1). Additionally, a semi-iterative smoother is constructed which gives, in some sense, optimal smoothing rate estimates.
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  • 51
    Digitale Medien
    Digitale Medien
    Conference diary (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 179-183 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030202
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  • 52
    Digitale Medien
    Digitale Medien
    Parallel Algorithms for Orthotropic Problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 185-203 
    Details
    ISSN: 1070-5325
    Schlagwort(e): orthotropic partial differential equation ; preconditioned conjugate gradient method ; parallel algorithm ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Finite element meshes and node-numberings suitable for parallel solution with equally loaded processors are presented for linear orthotropic elliptic partial differential equations. These problems are of great importance, for instance in the oil and airfoil industries. The linear systems of equations are solved by the conjugate gradient method preconditioned by modified incomplete factorization, MIC. The basic method presented, is based on fronts of uncoupled nodes and unlike earlier methods it has the advantage of no requirement of a specific orientation of the mesh. This method is however, in general, restricted to small degree of anisotropy in the differential equation. Another method, which does not suffer from this limitation, uses rotation of the differential equation and spectral equivalence. The rotation is made in such a way that in the new co-ordinate system, the basic method is applicable. The spectral equivalence property is used for estimation of the condition number of the preconditioned system. Both methods are suitable for implementation on parallel computers. The computer architecture could be single instruction multiple data (SIMD) as well as multiple instruction multiple data (MIMD) with shared or distributed memory. Implementation of the basic method on a shared memory parallel computer shows a significant improvement by use of the MIC method compared with the diagonal scaling preconditioning method.
    Zusätzliches Material: 13 Ill.
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  • 53
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    Digitale Medien
    Overlapping Domain Decomposition Algorithms for General Sparse Matrices (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 221-237 
    Details
    ISSN: 1070-5325
    Schlagwort(e): sparse matrix ; iterative methods ; preconditioning ; graph partitioning ; domain decomposition ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Domain decomposition methods for finite element problems using a partition based on the underlying finite element mesh have been extensively studied. In this paper, we discuss algebraic extensions of the class of overlapping domain decomposition algorithms for general sparse matrices. The subproblems are created with an overlapping partition of the graph corresponding to the sparsity structure of the matrix. These algebraic domain decomposition methods are especially useful for unstructured mesh problems. We also discuss some difficulties encountered in the algebraic extension, particularly the issues related to the coarse solver.
    Zusätzliches Material: 4 Ill.
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  • 54
    Digitale Medien
    Digitale Medien
    Convergence Estimates of Multilevel Additive and Multiplicative Algorithms for Non-symmetric and Indefinite Problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 205-220 
    Details
    ISSN: 1070-5325
    Schlagwort(e): elliptic equations ; multilevel methods ; finite element ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: New uniform estimates for multigrid algorithms are established for certain non-symmetric indefinite problems. In particular, we are concerned with the simple additive algorithm and multigrid (V(1,0)-cycle) algorithms given in [5]. We prove, without full elliptic regularity assumption, that these algorithms have uniform reduction per iteration, independent of the finest mesh size and number of refinement levels, provided that the coarsest mesh size is sufficiently small.
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  • 55
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    Digitale Medien
    Masthead (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030301
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  • 56
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    Digitale Medien
    Globalization of Newton's Method for Solving Non-linear Equations (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 239-249 
    Details
    ISSN: 1070-5325
    Schlagwort(e): non-linear equations ; global convergence ; Lagrangians ; non-linear programming ; Lagrangian globalization ; detour potentials ; homotopy methods ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Lagrangian globalization (LG) method for non-linear equation-solving proposed in [10] is developed through theoretical analysis, the formulation of a particular LG algorithm, and a numerical illustration. New merit functions (termed detour potentials) for non-linear equation-solving, which broaden the LG concept, are also defined.
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  • 57
    Digitale Medien
    Digitale Medien
    Conference diary (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 251-254 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680030302
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  • 58
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    Digitale Medien
    Two-level Preconditioner with Small Coarse Grid Appropriate for Unstructured Meshes (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 255-274 
    Details
    ISSN: 1070-5325
    Schlagwort(e): conjugate gradient method ; preconditioning ; two-level method ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The presented paper contains a suggestion and an analysis of a two-level preconditioner appropriate for unstructured meshes. The convergence analysis is done for H1-equivalent forms in the two-dimensional case; ways for generalization are discussed, too. The efficiency is demonstrated by numerical experiments.
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  • 59
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    Digitale Medien
    DQGMRES: a Direct Quasi-minimal Residual Algorithm Based on Incomplete Orthogonalization (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 329-343 
    Details
    ISSN: 1070-5325
    Schlagwort(e): iterative methods ; GMRES ; Krylov methods ; incomplete orthogonalization ; quasi-minimization ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We describe a Krylov subspace technique, based on incomplete orthogonalization of the Krylov vectors, which can be considered as a truncated version of GMRES. Unlike GMRES(m), the restarted version of GMRES, the new method does not require restarting. Like GMRES, it does not break down. Numerical experiments show that DQGMRES(k) often performs as well as the restarted GMRES using a subspace of dimension m=2k. In addition, the algorithm is flexible to variable preconditioning, i.e., it can accommodate variations in the preconditioner at every step. In particular, this feature allows the use of any iterative solver as a right-preconditioner for DQGMRES(k). This inner-outer iterative combination often results in a robust approach for solving indefinite non-Hermitian linear systems.
    Zusätzliches Material: 9 Tab.
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  • 60
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    Digitale Medien
    A Regularization Procedure for Σn-i=1fi(zj)xi = g(zj), ( j = 1, 2, …, n) (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 81-90 
    Details
    ISSN: 1070-5325
    Schlagwort(e): linear systems ; regularization ; divided differences ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A regularization procedure for linear systems of the type fi(zj)xi = g(zj), (j = 1, 2, …, n) is presented, which is particularly useful in the case when z1, z2, …, zn are close to each other. The associated numerical algorithm was tested on several examples for which analytic solutions do exist and was found to yield highly accurate results.
    Zusätzliches Material: 1 Ill.
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  • 61
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    Digitale Medien
    Low-rank Orthogonal Decompositions for Information Retrieval Applications (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 301-327 
    Details
    ISSN: 1070-5325
    Schlagwort(e): information ; latent semantic indexing ; low-rank ; orthogonal ; matrices ; metrieval ; singular value decomposition ; sparse ; ULV and URV decompositions ; updating ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Current methods to index and retrieve documents from databases usually depend on a lexical match between query terms and keywords extracted from documents in a database. These methods can produce incomplete or irrelevant results due to the use of synonyms and polysemus words. The association of terms with documents (or implicit semantic structure) can be derived using large sparse {\it term-by-document} matrices. In fact, both terms and documents can be matched with user queries using representations in k-space (where 100 ≤ k ≤ 200) derived from k of the largest approximate singular vectors of these term-by-document matrices. This completely automated approach called latent semantic indexing or LSI, uses subspaces spanned by the approximate singular vectors to encode important associative relationships between terms and documents in k-space. Using LSI, two or more documents may be closeto each other in k-space (and hence meaning) yet share no common terms. The focus of this work is to demonstrate the computational advantages of exploiting low-rank orthogonal decompositions such as the ULV (or URV) as opposed to the truncated singular value decomposition (SVD) for the construction of initial and updated rank-k subspaces arising from LSI applications.
    Zusätzliches Material: 11 Ill.
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  • 62
    Digitale Medien
    Digitale Medien
    A Multigrid Method Based on Incomplete Gaussian Elimination (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 369-390 
    Details
    ISSN: 1070-5325
    Schlagwort(e): multigrid ; incomplete Gaussian elimination ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we introduce and analyse a new Schur complement approximation based on incomplete Gaussian elimination. The approximate Schur complement is used to develop a multigrid method. This multigrid method has an algorithmic structure that is very similar to the algorithmic structure of classical multigrid methods. The resulting method is almost purely algebraic and has interesting properties with respect to variation in problem parameters.
    Zusätzliches Material: 5 Ill.
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  • 63
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    Digitale Medien
    Multilevel Minimal Residual Methods for Nonsymmetric Elliptic Problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 351-367 
    Details
    ISSN: 1070-5325
    Schlagwort(e): multilevel preconditioning ; Krylov subspace methods ; GMRES, nonsymmetric elliptic problems ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The subject of this paper is to study the performance of multilevel preconditioning for nonsymmetric elliptic boundary value problems. In particular, a minimal residual method with respect to an appropriately scaled norm, measuring the size of the residual projections on all levels, is studied. This norm, induced by the multilevel splitting, is also the basis for a proper stopping criterion. Our analysis shows that the convergence rate of this minimal residual method using the multilevel preconditioner by Bramble, pasciak and Xu is bounded independently of the mesh-size. However, the convergence rate deteriorates with increasing size of the skew-symmetric part. Our numerical results show that by incorporating this into a multilevel cycle starting on the coarsest level, one can save fine-level-iterations and, therefore, computational work.
    Zusätzliches Material: 2 Ill.
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  • 64
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    Digitale Medien
    Approximate solutions and eigenvalue bounds from Krylov subspaces (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 115-133 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Krylov subspace ; Lanczos process ; symmetric matrix ; conjugate gradients ; minimum residual ; Lehmann intervals ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Approximations to the solution of a large sparse symmetric system of equations are considered. The conjugate gradient and minimum residual approximations are studied without reference to their computation. Several different bases for the associated Krylov subspace are used, including the usual Lanczos basis. The zeros of the iteration polynomial for the minimum residual approximation (harmonic Ritz values) are characterized in several ways and, in addition, attractive convergence properties are established. The connection of these harmonic Ritz values to Lehmann's optimal intervals for eigenvalues of the original matrix appears to be new.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020205
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  • 65
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    Digitale Medien
    Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 155-171 
    Details
    ISSN: 1070-5325
    Schlagwort(e): condition number ; norm of a matrix ; matrix completion ; dilation theory ; robust regularization of descriptor systems ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020207
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  • 66
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    Digitale Medien
    Conference diary (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 191-194 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020209
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  • 67
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    Digitale Medien
    Stability of block LU factorization (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 173-190 
    Details
    ISSN: 1070-5325
    Schlagwort(e): block algorithm ; LAPACK ; level 3 BLAS ; iterative refinement ; LU factorization ; backward error analysis ; block diagonal dominance ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Many of the currently popular ‘block algorithms’ are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by columns. Moreover, for a general matrix the level of instability in block LU factorization can be bounded in terms of the condition number K(A) and the growth factor for Gaussian elimination without pivoting. A consequence is that block LU factorization is stable for a matrix A that is symmetric positive definite or point diagonally dominant by rows or columns as long as A is well-conditioned.
    Zusätzliches Material: 4 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020208
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  • 68
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    Digitale Medien
    Orthogonal projection and total least squares (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 135-153 
    Details
    ISSN: 1070-5325
    Schlagwort(e): orthogonal projection ; numerical rank ; total least squares ; rank revealing QR factorization ; acute perturbation ; subspace angle ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Overdetermined linear systems often arise in applications such as signal processing and modern communication. When the overdetermined system of linear equations AX ≍ B has no solution, compatibility may be restored by an orthogonal projection method. The idea is to determine an orthogonal projection matrix P by some method M such that [à B̃] = P[A B], and ÃX = B̃ is compatible. Denote by XM the minimum norm solution to ÃX = B̃ using method M. In this paper conditions for compatibility of the lower rank approximation and subspace properties of à in relation to the nearest rank-k matrix to A are discussed. We find upper and lower bounds for the difference between the solution XM and the SVD-based total least squares (TLS) solution XSVD and also provide a perturbation result for the ordinary TLS method. These results suggest a new algorithm for computing a total least squares solution based on a rank revealing QR factorization and subspace refinement. Numerical simulations are included to illustrate the conclusions.
    Zusätzliches Material: 4 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020206
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  • 69
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    Digitale Medien
    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020301
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  • 70
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    Digitale Medien
    Some inverse eigenproblems for Jacobi and arrow matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 195-203 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Jacobi matrix ; arrow matrix ; inverse problem ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the problem of reconstructing Jacobi matrices and real symmetric arrow matrices from two eigenpairs. Algorithms for solving these inverse problems are presented. We show that there are reasonable conditions under which this reconstruction is always possible. Moreover, it is seen that in certain cases reconstruction can proceed with little or no cancellation. The algorithm is particularly elegant for the tridiagonal matrix associated with a bidiagonal singular value decomposition.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020302
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  • 71
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    Digitale Medien
    Trust regions based on conic functions in linear and nonlinear programming (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 235-241 
    Details
    ISSN: 1070-5325
    Schlagwort(e): interior-point methods ; trust regions ; conic functions ; conjugate gradients ; linear programming ; nonlinear minimization ; Karmarkar's algorithm ; centering ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An optimization method is developed based on ellipsoidal trust regions that are defined by conic functions. It provides a powerful unifying theory from which can be derived a variety of interesting and potentially useful optimization algorithms, in particular, conjugate-gradient-like algorithms for nonlinear minimization and Karmarkar-like interior-point algorithms for linear programming.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020305
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  • 72
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    Digitale Medien
    Progress in the numerical solution of the nonsymmetric eigenvalue problem (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 219-234 
    Details
    ISSN: 1070-5325
    Schlagwort(e): nonsymmetric matrices ; sparse matrices ; eigenvalue problem ; EISPACK ; LAPACK ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: With the growing demands from disciplinary and interdisciplinary fields of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper we examine the state of the art of the algorithmic techniques and the software scene for the problem. Some current developments are also outlined.
    Zusätzliches Material: 2 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020304
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  • 73
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    Digitale Medien
    Regions of convergence of the Rayleigh quotient iteration method (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 251-269 
    Details
    ISSN: 1070-5325
    Schlagwort(e): eigenvalues ; eigenvectors ; symmetric matrices ; Rayleigh quotient iteration ; convergence ; basins of attraction ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Rayleigh quotient iteration method finds an eigenvector and the corresponding eigenvalue of a symmetric matrix. This is a fundamental problem in science and engineering. Parlett and Kahan have shown, in 1968, that for almost any initial vector in the unit sphere, the Rayleigh quotient iteration method converges to some eigenvector. In this paper, the regions of the unit sphere which include all possible initial vectors converging to a specific eigenvector are studied. The generalized eigenvalue problem Ax = λBx is considered. It is shown that the regions do not change when the matrix is shifted or multiplied by a scalar. These regions are completely characterized in the three-dimensional case. It is shown that, in this case, the area of the region of convergence corresponding to the interior eigenvalue is larger than the area of those corresponding to any extreme one. This can be interpreted, with the appropriate choice of probability distribution, as: the probability of converging to an eigenvector corresponding to the interior eigenvalue is larger than the probability of converging to an eigenvector corresponding to any extreme eigenvalue. It is conjectured that the same is true for matrices of any order. Experiments in higher dimensions are presented which conform with the conjecture.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020307
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  • 74
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    Digitale Medien
    Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 205-217 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Lanczos method ; spectral Lanczos ; decompostion method ; eigenpairs ; matrix functions ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Many researchers are now working on computing the product of a matrix function and a vector, using approximations in a Krylov subspace. We review our results on the analysis of one implementation of that approach for symmetric matrices, which we call the spectral lanczos decomposition method (SLDM).We have proved a general convergence estimate, relating SLDM error bounds to those obtained through approximation of the matrix function by a part of its Chebyshev series. Thus, we arrived at effective estimates for matrix functions arising when solving parabolic, hyperbolic and elliptic partial differential equations. We concentrate on the parabolic case, where we obtain estimates that indicate superconvergence of SLDM. For this case a combination of SLDM and splitting methods is also considered and some numerical results are presented.We implement our general estimates to obtain convergence bounds of Lanczos approximations to eigenvalues in the internal part of the spectrum. Unlike Kaniel-Saad estimates, our estimates are independent of the set of eigenvalues between the required one and the nearest spectrum bound.We consider an extension of our general estimate to the case of the simple Lanczos method (without reorthogonalization) in finite computer arithmetic which shows that for a moderate dimension of the Krylov subspace the results, proved for the exact arithmetic, are stable up to roundoff.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020303
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  • 75
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    Digitale Medien
    Announcement and call for papers (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 311-312 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020311
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  • 76
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    Digitale Medien
    Conference diary (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 313-315 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020312
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    Dynamical analysis of numerical systems (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 297-310 
    Details
    ISSN: 1070-5325
    Schlagwort(e): dynamical systems ; eigenvalues ; QR algorithm ; Francis shift ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: For many years techniques from numerical analysis have been applied fruitfully to the study of dynamical systems. In this paper it is shown that the theory of dynamical systems may be applied to certain computational problems. In particular the question of global convergence of various QR algorithms can be reduced to the study of certain vector iterations derived from Schur forms of matrices. The technique is illustrated in determining the convergence behavior of normal Hessenberg matrices under the Francis and multishift QR iterations.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020310
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    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020401
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    A comparison result for multisplittings and waveform relaxation methods (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 335-346 
    Details
    ISSN: 1070-5325
    Schlagwort(e): multisplittings ; overlapping ; comparison results ; M-matrices ; waveform relaxation ; parallel algorithms ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M-matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC/860 hypercube are included.
    Zusätzliches Material: 2 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020403
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  • 80
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    A spectral algorithm for envelope reduction of sparse matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 317-334 
    Details
    ISSN: 1070-5325
    Schlagwort(e): envelope reduction ; eigenvalues of graphs ; Gibbs - King algorithm ; Gibbs - Poole - Stockmeyer algorithm ; Laplacian matrices ; reordering algorithms ; reverse Cuthill - McKee algorithm ; sparse matrices ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reording algorithm usually computes smaller envelope sizes than those obtained from the current standards such as the Gibbs - Poole - Stockmeyer (GPS) algorithm or the reverse Cuthill - McKee (RCM) algorithm in SPARSPAK, in some cases reducing the envelope by more than a factor of two.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020402
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  • 81
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    The RSCG algorithm on distributed memory architectures (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 401-414 
    Details
    ISSN: 1070-5325
    Schlagwort(e): conjugate gradient ; distributed computing ; analytic model ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we demonstrate the scalability of the Reduced System Conjugate Gradient (RSCG) algorithm on distributed memory architectures. We present speed-up results obtained on the Intel iPSC/860 that compare one-, two-, and three-dimensional decompositions of the domain for both positive definite and positive semidefinite test problems. We develop a model for the RSCG algorithm to analyze computational and communication costs. The model is validated using experimental data and then used to examine and predict behavior of the RSCG algorithm as a function of architecture parameters including communication latency and transmission times and memory access costs.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020503
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  • 82
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    Announcement and call for papers (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 481-481 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020508
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  • 83
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    On a generalized conjugate gradient orthogonal residual method (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 467-479 
    Details
    ISSN: 1070-5325
    Schlagwort(e): generalized conjugate gradient ; orthogonal residual ; rate of convergence ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: To solve a linear system of equations with a generally nonsymmetric matrix, a generalized conjugate gradientorthogonal residual method is presented. The method uses all previous search directions (or a truncated set of them) at each step but, contrary to standard implementations of similar methods, it requires storage of only one set with a linearly growing number of vectors (or the number in the truncated set). Furthermore, there is only one vector (the residual), which must be updated using all the vectors in this set, at each step. In this respect it is similar to the popular GMRES method but it has the additional advantage that it can stop at any stage when the norm of the residual is sufficiently small and no extra computation is needed to compute this norm. Furthermore, the new method can be truncated.The rate of convergence of the method is also discussed.
    Zusätzliches Material: 3 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020507
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  • 84
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    Digitale Medien
    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020601
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  • 85
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    Parallel computation of radiation view factors between two arbitrarily oriented surfaces (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 43-50 
    Details
    ISSN: 1069-8299
    Schlagwort(e): view factor ; radiation ; parallel computation ; heat transfer ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Two implementations for parallel computation of radiation heat transfer view factors are formulated and tested for a model problem. Using a sufficiently large number of processors and a suitable communications paradigm, the solution time for the problem considered here scales linearly with the number of surface elements in the parallel implementation rather than the quadratic scaling obtained using a serial approach. For larger problems, significantly shorter solution times are obtained using the massively parallel Connection Machine 5 than those obtained on a single processor of the Cray C-90, a traditional vector supercomputer. Parallel performance was degraded for implementations using too few processors or data layouts leading to inefficient processor communication.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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    A Taylor expansion algorithm for integration of 3D near-hypersingular integrals (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 51-62 
    Details
    ISSN: 1069-8299
    Schlagwort(e): boundary element method ; hypersingular integrals ; singular integration ; elasticity ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: An algorithm based on the Taylor series expansion is extended to deal with the problem of near-hypersingular integrals occurring in a 3D electrostatic BEM formulation. The integral is evaluated by subtracting out the leading terms in the near-hypersingular part of the integrand and adding it back. The accuracy of the proposed method is demonstrated for a curved element. It is shown that accurate values can be obtained with low orders of Gaussian quadrature.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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  • 87
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    Digitale Medien
    Masthead (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640120201
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  • 88
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    Conference diary (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 147-148 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640120202
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    Annoucement (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 149-150 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640120203
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  • 90
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    An asymptotic formula for correcting finite element predicted natural frequencies of membrane vibration problems (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 63-73 
    Details
    ISSN: 1069-8299
    Schlagwort(e): asymptotic solution ; natural frequencies ; membrane vibrations ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In the paper an asymptotic formula has been developed to correct the discretization error for the finite element predicted natural frequencies of membrane transverse vibration problems. The general idea behind deriving this asymptotic formula is that, when the finite element size approaches zero, a discretized finite element system approaches a continuous system and the predicted natural frequencies of the system from the finite element analysis therefore approach the exact solutions of the system. Without losing generality, several different finite element mesh patterns have been considered and the same asymptotic formula for correcting the finite element predicted natural frequency has been obtained for all the different mesh patterns because of the uniqueness of the exact solution to the natural frequency of a real structure. The usefulness, effectiveness and efficiency of the present asymptotic formula have been assessed by a simple but critical problem, for which the exact solution is available for comparison. In order to investigate the applicability of the asymptotic formula to practical engineering problems, two challenging membrane vibration problems of irregular shapes, an L-shape and a tapered shape with a circular hole in the centre, have also been analysed. The related numerical results have demonstrated that the asymptotic formula provides a very useful post-processing error corrector for the finite element predicted natural frequencies of membrane transverse vibration problems, even though the problem domains are of irregular shape. The greatest advantage in using the present asymptotic formula is that it yields a solution of higher accuracy, by simply using the formula to correct the rough solution obtained from a much coarser finite element mesh with fewer degrees of freedom, without any further finite element calculation.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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    Eigenvalue extraction for large finite element models using a new conjugate gradient algorithm (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 77-83 
    Details
    ISSN: 1069-8299
    Schlagwort(e): eigenvalue extraction ; conjugate gradient method ; finite element method ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A new conjugate gradient algorithm is presented for extracting eigenvalues from large systems of equations encountered in finite element analysis. The new algorithm involves applying the conjugate gradient method (CGM) to a static problem to generate an equivalent tridiagonal matrix used for eigenvalue computation. The eigenvalues of the tridiagonal matrix are then extracted using a QR factorization. The similarity of the new CGM with the Lanczos method is discussed regarding the need for matrix inversion and reorthogonalization. Several examples using the new method are presented to illustrate its performance.
    Zusätzliches Material: 2 Ill.
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  • 92
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    Digitale Medien
    A direct method to derive the boundary conditions of the homogenization equation for symmetric cells (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 185-196 
    Details
    ISSN: 1069-8299
    Schlagwort(e): homogenization ; boundary conditions ; periodicity ; finite element ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The numerical solution of homogenization equations by the finite element (FE) method is explained briefly. The issue of extracting boundary conditions from the periodicity assumption is addressed and a direct method utilizing symmetry is presented. Using this method, the computation of the elements of the constitutive matrix of a composite material is reduced to a very conventional boundary value problem with known forces and boundary conditions which can be carried out with any FE code. Two examples are presented.
    Zusätzliches Material: 15 Ill.
    Materialart: Digitale Medien
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  • 93
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    Digitale Medien
    Masthead (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640120401
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  • 94
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    Digitale Medien
    Best-fit stress performance of a higher-order beam element (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 229-234 
    Details
    ISSN: 1069-8299
    Schlagwort(e): higher-order beam element ; best-fit stress prediction ; a priori error analysis ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: It is known that finite elements try to capture stresses within each discretized local region in a ‘best-fit’ sense. In the paper we examine the performance of a beam element based on a higher-order shear deformation theory and show that the best-fit paradigm accounts for the manner in which through-the-thickness displacement and stresses are modelled. An a priori prediction derived from the paradigm is confirmed by a carefully chosen numerical experiment. This provides a measure of the quality of approximation as well as another ‘falsification’ of the best-fit paradigm.
    Zusätzliches Material: 1 Ill.
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  • 95
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    A different approach to discretization for the numerical simulation of three-dimensional heat conduction in irregularly shaped materials (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 223-228 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Discretization ; heat conduction ; simulation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A different approach to discretization is described with which complicated three-dimensional heat transfer problems can be solved with a finite volume approach on a general curvilinear grid. It represents an improvement on the existing methods in that it can easily be expanded to three-dimensional problems. A concise explanation of the transformation process is given, together with a discussion of the discretization procedure. The method is evaluated by solving two simple test problems and comparing the results with those of existing methods and the analytical solution. In conclusion it is found that this method yields equally or more accurate results than the existing methods, with the additional advantage of being easily expandable to three-dimensional problems.
    Zusätzliches Material: 5 Ill.
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  • 96
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    Digitale Medien
    Automatic nodes generation in N-dimensional space (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 243-248 
    Details
    ISSN: 1069-8299
    Schlagwort(e): finite elements ; automatic generation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Finite element generation methods, such as Delaunay, allow the meshing of shapes from a set of nodes. These nodes must previously exist. The authors present a simple, fast and reliable method to generate them in an unstructured way in N-dimensional space. Its main characteristic is to easily allow variation of the node density by introducing a density function, either analytical or discretized. This function can also be anisotropic. Some nodes can have a pre-fixed position. Inner lines and holes can also be specified in the domain to be meshed. Generated nodes are to be connected according to triangles in 2D and tetrahedrals in 3D.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 97
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    A modified non-linear member element allowing large loading and displacement increments (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 235-242 
    Details
    ISSN: 1069-8299
    Schlagwort(e): finite member element ; modified theory ; geometrical non-linearity ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In the paper a modified non-linear member element is derived which can lead to satisfactory computed results even for large loading and displacement increments from pre-instability to post-instability of structures. The high accuracy of this element is proved by numerical examples.
    Zusätzliches Material: 4 Ill.
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    Digitale Medien
    Masthead (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640120501
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  • 99
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    Digitale Medien
    Quadratic programming algorithms for obstacle problems (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 249-256 
    Details
    ISSN: 1069-8299
    Schlagwort(e): obstacle problems ; quadratic programming ; finite element ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The numerical solution of problems involving frictionless contact between an elastic body and a rigid obstacle is considered. The elastic body may undergo small or large deformation. Finite element discretization and repetitive linearization lead to a sequence of quadratic programming (QP) problems for incremental displacement. The performances of several QP algorithms, including two new versions of a modified steepest descent algorithm, are compared in this context. Numerical examples include a string, a membrane and an Euler-Bernoulli beam, in contact with flat and non-flat rigid obstacles.
    Zusätzliches Material: 2 Ill.
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  • 100
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    Digitale Medien
    Conference diary (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 317-319 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640120502
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