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Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems

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Abstract

We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix–vector products per iteration without accessing AT. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal [15] (without look-ahead), which requires three matrix–vector products per iteration. We also present a related transpose-free version of the bi-conjugate gradients algorithm.

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Authors and Affiliations

  1. Department of Mathematics, UCLA, Los Angeles, CA, 90095-1555, USA

    Tony F. Chan

  2. Department of Mathematics, Harvey Mudd College, Claremont, CA, 91711-5990, USA

    Lisette de Pillis

  3. Mathematical Institute, University of Utrecht, Budapestlaan 6, Utrecht, The Netherlands

    Henk van der Vorst

Authors
  1. Tony F. Chan
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  2. Lisette de Pillis
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  3. Henk van der Vorst
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Chan, T.F., de Pillis, L. & van der Vorst, H. Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems. Numerical Algorithms 17, 51–66 (1998). https://doi.org/10.1023/A:1011637511962

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