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Preconditioners for nonsymmetric block toeplitz-like-plus-diagonal linear systems

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Summary.

We consider the system of linear equations Lu=f, where L is a nonsymmetric block Toeplitz-like-plus-diagonal matrix, which arises from the Sinc-Galerkin discretization of differential equations. Our main contribution is to construct effective preconditioners for this structured coefficient matrix and to derive tight bounds for eigenvalues of the preconditioned matrices. Moreover, we use numerical examples to show that the new preconditioners, when applied to the preconditioned GMRES method, are efficient for solving the system of linear equations.

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Authors and Affiliations

  1. State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, The People’s Republic of China

    Zhong-Zhi Bai

  2. Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

    Michael K. Ng

Authors
  1. Zhong-Zhi Bai
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  2. Michael K. Ng
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Correspondence to Michael K. Ng.

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Mathematics Subject Classification (2000): 65F10, 65F15, 65T10

Research subsidized by The Special Funds for Major State Basic Research Projects G1999032803

Research supported in part by RGC Grant Nos. 7132/00P and 7130/02P, and HKU CRCG Grant Nos 10203501, 10203907 and 10203408

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Bai, ZZ., Ng, M. Preconditioners for nonsymmetric block toeplitz-like-plus-diagonal linear systems. Numer. Math. 96, 197–220 (2003). https://doi.org/10.1007/s00211-003-0454-0

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  • DOI: https://doi.org/10.1007/s00211-003-0454-0

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