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  • Engineering General  (1)
  • Matrix functions  (1)
  • 1995-1999  (2)
  • 1
    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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  • 2
    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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