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  • Articles  (10)
  • CR: 5.14  (10)
  • Springer  (10)
  • American Chemical Society (ACS)
  • Elsevier
  • 2005-2009
  • 1990-1994
  • 1980-1984  (10)
  • 1980  (10)
  • Mathematics  (10)
  • Geography
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  • Articles  (10)
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  • Springer  (10)
  • American Chemical Society (ACS)
  • Elsevier
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  • 2005-2009
  • 1990-1994
  • 1980-1984  (10)
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  • Mathematics  (10)
  • Geography
  • 1
    Electronic Resource
    Electronic Resource
    Reguläre Zerlegungen und Berechnung des Spektralradius nichtnegativer Matrizen (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 201-216 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary On the basis of a Rayleigh Quotient Iteration method in [10] and a Maximal Quotient Iteration method in [5, 8] two algorithms for solving special eigenvalue problems are developed. The characteristic properties of these methods lie in the application of iterative linear methods to solving systems of linear equations. The convergence properties are investigated. We apply the algorithms to the computation of the spectralradius of a nonnegative irreducible matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396060
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  • 2
    Electronic Resource
    Electronic Resource
    Realistic error bounds for a simple eigenvalue and its associated eigenvector (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 113-126 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F15 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An algorithm is described which, given an approximate simple eigenvalue and a corresponding approximate eigenvector, provides rigorous error bounds for improved versions of them. No information is required on the rest of the eigenvalues, which may indeed correspond to non-linear elementary divisors. A second algorithm is described which gives more accurate improved versions than the first but provides only error estimates rather than rigorous bounds. Both algorithms extend immediately to the generalized eigenvalue problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396310
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  • 3
    Electronic Resource
    Electronic Resource
    Characterizations of dominant and dominated solutions of linear recursions (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 421-442 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65Q05, 65F99, 39A10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Dominated solutions of a linear recursion (i.e. solutions which are outgrown by other ones) cannot be computed in a stable way by forward recursion. We analyze this dominance phenomenon more closely and give practically significant characterizations for dominated and dominant solutions. For a dominated solution, in particular, this leads to a stable computational method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399009
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  • 4
    Electronic Resource
    Electronic Resource
    Stability of fast algorithms for matrix multiplication (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 63-72 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 15A63 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Non commutative fast algorithms to compute 2×2 matrix product are classified with regard to stability. An analysis of the rounding error propagation is presented for then×n matrix multiplication algorithms obtained by recursive partitioning.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395989
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  • 5
    Electronic Resource
    Electronic Resource
    Least squares with a quadratic constraint (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 291-307 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F20 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present the theory of the linear least squares problem with a quadratic constraint. New theorems characterizing properties of the solutions are given. A numerical application is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396656
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  • 6
    Electronic Resource
    Electronic Resource
    Matrices related to interpolatory quadratures (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 309-318 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65F15 ; 65D30 ; CR: 5.14 ; 5.16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An explicit formula for the coefficients of interpolatory quadratures with knots of arbitrary multiplicity which uses the eigenvectors and principal vectors of certain matrices is derived. The construction and properties of such matrices are discussed, and applications for the evaluation of Gauss and generalized Gauss-Lobatto quadratures are indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396657
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  • 7
    Electronic Resource
    Electronic Resource
    An algorithm for a linear diophantine equation and a problem of Frobenius (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 349-352 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 10B05 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We solve the diophantine equation $$\sum\limits_{j = 1}^n {a_j x_j } = L$$ for nonnegative variablesx j , wherea j andL are positive integers. We characterize both the values ofL that lead to solutions and those that do not lead to solutions. We solve the Frobenius problem of finding the largest value ofL for which no solution exists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403673
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  • 8
    Electronic Resource
    Electronic Resource
    A generalization of the Stein-Rosenberg theorem to Banach spaces (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 403-409 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS):65F 10, 47B 55 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In the first part of this note we prove a generalization of the Stein-Rosenberg theorem; the context is that of real Banach spaces with a normal reproducing cone and the operators involved are positive and completely continuous. Our generalization of the Stein-Rosenberg theorem improves the modern version of it as stated by F. Robert in [5, §2]. In the second part, we discuss briefly how our results are related to other versions of the Stein-Rosenberg theorem. In the last section we describe a situation to which the results in the first part can be applied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403677
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  • 9
    Electronic Resource
    Electronic Resource
    On the sharpness of some upper bounds for the spectral radii of S.O.R. iteration matrices (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 69-79 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Sharpness is shown for three upper bounds for the spectral radii of point S.O.R. iteration matrices resulting from the splitting (i) of a nonsingularH-matrixA into the ‘usual’D−L−U, and (ii) of an hermitian positive definite matrixA intoD−L−U, whereD is hermitian positive definite andL=1/2(A−D+S) withS some skew-hermitian matrix. The first upper bound (which is related to the splitting in (i)) is due to Kahan [6], Apostolatos and Kulisch [1] and Kulisch [7], while the remaining upper bounds (which are related to the splitting in (ii)) are due to Varga [11]. The considerations regarding the first bound yield an answer to a question which, in essence, was recently posed by Professor Ridgway Scott: What is the largest interval in ω, ω≧0, for which the point S.O.R. iterative method is convergent for all strictly diagonally dominant matrices of arbitrary order? The answer is, precisely, the interval (0, 1].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396371
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  • 10
    Electronic Resource
    Electronic Resource
    The rate of convergence of an approximate matrix factorization semi-direct method (1980)
    Springer
    Numerische Mathematik 36 (1980), S. 237-251 
    Details
    ISSN: 0945-3245
    Keywords: CR: 5.14 ; 5.17 ; AMS(MOS): 65F10 ; 65N10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The definition of acceleration parameters for the convergence of a sparseLU factorization semi-direct method is shown to be based on lower and upper bounds of the extreme eigevalues of the iteration matrix. Optimum values of these parameters are established when the eigenvalues of the iteration matrix are either real or complex. Estimates for the computational work required to reduce theL 2 norm of the error by a specified factor ɛ are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396653
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