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Approximation of matrix operators applied to multiple vectors

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  • Hochbruck, Marlis
  • Niehoff, Jörg

Abstract

In this paper we propose a numerical method for approximating the product of a matrix function with multiple vectors by Krylov subspace methods combined with a QR decomposition of these vectors. This problem arises in the implementation of exponential integrators for semilinear parabolic problems. We will derive reliable stopping criteria and we suggest variants using up- and downdating techniques. Moreover, we show how Ritz vectors can be included in order to speed up the computation even further. By a number of numerical examples, we will illustrate that the proposed method will reduce the total number of Krylov steps significantly compared to a standard implementation if the vectors correspond to the evaluation of a smooth function at certain quadrature points.

Suggested Citation

  • Hochbruck, Marlis & Niehoff, Jörg, 2008. "Approximation of matrix operators applied to multiple vectors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1270-1283.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:4:p:1270-1283
    DOI: 10.1016/j.matcom.2008.03.016
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