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A minimum residual algorithm for solving linear systems

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Abstract

A minimum residual algorithm for solving a large linear system (I+S)x=b, with b∈ℂn and S∈ℂn×n being readily invertible, is proposed. For this purpose Krylov subspaces are generated by applying S and S -1 cyclically. The iteration can be executed with every linear system once the coefficient matrix has been split into the sum of two readily invertible matrices. In case S is a translation and a rotation of a Hermitian matrix, a five term recurrence is devised.

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Authors and Affiliations

  1. Institute of Mathematics, Helsinki University of Technology, Box 1100, FIN-02015, Helsinki, Finland

    Marko Huhtanen

  2. Institute of Mathematics, Helsinki University of Technology, Box 1100, FIN-02015, Helsinki, Finland

    Olavi Nevanlinna

Authors
  1. Marko Huhtanen
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  2. Olavi Nevanlinna
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Correspondence to Marko Huhtanen.

Additional information

In memory of Germund Dahlquist (1925–2005).

AMS subject classification (2000)

65F10

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Huhtanen, M., Nevanlinna, O. A minimum residual algorithm for solving linear systems . Bit Numer Math 46, 533–548 (2006). https://doi.org/10.1007/s10543-006-0073-0

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  • DOI: https://doi.org/10.1007/s10543-006-0073-0

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