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  • 1
    Monograph available for loan
    Monograph available for loan
    Matrix computations (1996)
    Baltimore [u.a.] : Johns Hopkins Univ. Press
    Details Availability
    Call number: 19/M 97.0071
    Type of Medium: Monograph available for loan
    Pages: xxvii, 694 S.
    Edition: 3rd ed.
    ISBN: 0801854148
    Series Statement: John Hopkins studies in the mathematical sciences
    Classification:
    C.1.8.
    Language: English
    Location: Reading room
    Branch Library: GFZ Library
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  • 2
    Electronic Resource
    Electronic Resource
    Bounds for the Entries of Matrix Functions with Applications to Preconditioning (1999)
    Springer
    BIT 39 (1999), S. 417-438 
    Details
    ISSN: 1572-9125
    Keywords: Matrix functions ; quadrature rules ; Lanczos process ; band matrices ; exponential decay ; preconditioned conjugate gradients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let A be a symmetric matrix and let f be a smooth function defined on an interval containing the spectrum of A. Generalizing a well-known result of Demko, Moss and Smith on the decay of the inverse we show that when A is banded, the entries of f(A)are bounded in an exponentially decaying manner away from the main diagonal. Bounds obtained by representing the entries of f(A)in terms of Riemann-Stieltjes integrals and by approximating such integrals by Gaussian quadrature rules are also considered. Applications of these bounds to preconditioning are suggested and illustrated by a few numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022362401426
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  • 3
    Electronic Resource
    Electronic Resource
    Approximating dominant singular triplets of large sparse matrices via modified moments (1996)
    Springer
    Numerical algorithms 13 (1996), S. 123-152 
    Details
    ISSN: 1572-9265
    Keywords: Chebyshev semi-iterative method ; modified moments ; singular value decomposition ; sparse matrices ; 65K15 ; 65K50 ; 68P20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A procedure for determining a few of the largest singular values and corresponding singular vectors of large sparse matrices is presented. Equivalent eigensystems are solved using a technique originally proposed by Golub and Kent based on the computation of modified moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel implementations on a network of workstations. Although no obvious relationship between modified moments and the corresponding eigenvectors is known to exist, a scheme to approximate both eigenvalues and eigenvectors (and subsequently singular values and singular vectors) has been produced. This scheme exploits both modified moments in conjunction with the Chebyshev semi-iterative method and deflation techniques to produce approximate eigenpairs of the equivalent sparse eigensystems. The performance of an ANSI-C implementation of this scheme on a network of UNIX workstations and a 256-processor Cray T3D is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02143130
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  • 4
    Electronic Resource
    Electronic Resource
    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
    Keywords: QR algorithm ; zero pattern ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680020203
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