research-article

Complete stagnation of GMRES for normal matrices

Authors:

Faranges Kyanfar,

Mahmoud Mohseni Moghadam,

Abbas SalemiAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 263, Issue C

Pages 417 - 422

Published: 01 June 2014 Publication History

Abstract

In this paper we study the problem of complete stagnation of the generalized minimum residual (GMRES) method for normal matrices. We first characterize all n í n nonsingular normal matrices A such that GMRES ( A, b ) stagnates completely for some vector b . Also we give necessary and sufficient conditions for the non-existence of a real stagnation vector for real normal matrices. The number of real stagnation vectors for normal matrices is studied. Moreover, we characterize all the eigenvalues of nonsingular normal matrices A M 3 ( C ) such that GMRES ( A, b ) stagnates completely for some b C 3 . Using the results derived by A. Greenbaum, V. Pták and Z. Strakoš in 1996, we consider the complete stagnation of unitary matrices and derive another characterization for all nonsingular normal matrices A M 3 ( R ) such that GMRES ( A, b ) stagnates completely for some vector b R 3 .

References

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Complete stagnation of GMRES for normal matrices
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
2. Theory of computation

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Published In

cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 263, Issue C

June 2014

517 pages

ISSN:0377-0427

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Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 June 2014

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