ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Selecting upwind parameters for improved iterative performance (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 235-242 
    Details
    ISSN: 1069-8299
    Keywords: upwinding ; iterative methods ; convection-diffusion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The effect of upwinding on iterative performance of convection-diffusion problems is investigated. An analysis of the iterative method considered here leads to a criterion for selecting the optimal upwinding parameter to improve iterative performance for a class of two-dimensional convection-diffusion problems. Supporting numerical experiments are presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110306
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    An explicit fourth-order compact finite difference scheme for three-dimensional convection-diffusion equation (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 209-218 
    Details
    ISSN: 1069-8299
    Keywords: three-dimensional convection-diffusion equation ; fourth-order compact scheme ; iterative methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present an explicit fourth-order compact finite difference scheme for approximating the three-dimensional convection-diffusion equation with variable coefficients. This 19-point formula is defined on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standard 7-point scheme in the context of basic iterative methods. Numerical examples are used to verify the fourth-order convergence rate of the scheme and to show that the Gauss-Seidel iterative method converges for large values of the convection coefficients. Some algebraic properties of the coefficient matrices arising from different discretization schemes are compared. We also comment on the potential use of the fourth-order compact scheme with multilevel iterative methods. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    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
    Keywords: iterative methods ; linear systems ; multisplittings ; overlap ; parallel algorithms ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    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
    Keywords: first-order PDEs ; iterative methods ; preconditioners ; Toeplitz ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    On M-multisplittings of singular M-matrices with application to Markov chains (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 299-311 
    Details
    ISSN: 1070-5325
    Keywords: iterative methods ; singular linear systems ; index of a matrix ; M-splittings ; multi-splittings ; Q-matrices ; Markov chains ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Given a singular M-matrix of a linear system, convergent conditions under which iterative schemes based on M-multisplittings are studied. Two of those conditions, the index of the iteration matrix and its spectral radius are investigated and related to those of the M-matrix. Furthermore, a parallel multisplitting iteration scheme for solving singular linear systems is suggested which can be applied to practical problems such as Poisson and elasticity problems under certain boundary conditions, the Neumann problem, and in Markov chains. A discussion of that multisplitting scheme, based on Gauss-Seidel type splittings is given for computing the stationary distribution vector of Markov chains. In this case a computational viable algorithm can be constructed, since only the nonsingularity of one weighting matrix of the multisplitting is needed. © 1998 John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    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
    Keywords: iterative methods ; GMRES ; Krylov methods ; incomplete orthogonalization ; quasi-minimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 9 Tab.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 7
    Electronic Resource
    Electronic Resource
    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
    Keywords: iterative methods ; linear systems ; singular matrices ; block methods ; multisplitting ; two-stage ; non-stationary ; Markov chains ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 8
    Electronic Resource
    Electronic Resource
    Operator trigonometry of the model problem (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 5 (1998), S. 377-399 
    Details
    ISSN: 1070-5325
    Keywords: iterative methods ; operator trigonometry ; anti-eigenvector ; Dirichlet problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The new operator-trigonometric theory for iterative linear solvers is illustrated by working out its details for the classical model problem for numerical partial differential equations: the Dirichlet problem on the unit square. Copyright © 1999 John Wiley & Sons, Ltd.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    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
    Keywords: sparse matrix ; iterative methods ; preconditioning ; graph partitioning ; domain decomposition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 10
    Electronic Resource
    Electronic Resource
    Operator trigonometry of iterative methods (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 4 (1997), S. 333-347 
    Details
    ISSN: 1070-5325
    Keywords: iterative methods ; operator trigonometry ; antieigenvalue ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new and general approach to the understanding and analysis of widely used iterative methods for the numerical solution of the equation Ax = b is presented. This class of algorithms, which includes CGN, GMRES. ORTHOMIN, BCG, CGS, and others of current importance, utilizes residual norm minimizing procedures, such as those often found under the general names Galerkin method, Arnoldi method, Lanczos method, and so on. The view here is different: the needed error minimizations are seen trigonometrically. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...