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On the role of orthogonality in the GMRES method

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SOFSEM'96: Theory and Practice of Informatics (SOFSEM 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1175))

Abstract

In the paper we deal with some computational aspects of the Generalized minimal residual method (GMRES) for solving systems of linear algebraic equations. The key question of the paper is the importance of the orthogonality of computed vectors and its influence on the rate of convergence, numerical stability and accuracy of different implementations of the method. Practical impact on the efficiency in the parallel computer environment is considered.

Part of this work was performed while the second author visited Department of Mathematics and Computer Science, Emory University, Atlanta, USA

This work was supported by the GA AS CR under grant 230401 and by the NSF grant Int 921824

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References

  1. R. Barret, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine and H. van der Vorst. Templates for the Solution of Linear Systems. SIAM, Philadelphia, 1994.

    Google Scholar 

  2. M. Benzi, M. Tůma: A sparse approximate inverse preconditioner for nonsymmetric linear systems. to appear in SIAM J. Sci. Comput.

    Google Scholar 

  3. T. Davis: Sparse matrix collection. NA Digest, Volume 94, Issue 42, October 1994.

    Google Scholar 

  4. J. Drkošová, A. Greenbaum, M. Rozložník, Z. Strakoš, Numerical Stability of the GMRES Method, BIT 3, pp. 309–330, 1995

    Google Scholar 

  5. R.W. Freund, G.H. Golub, N.M. Nachtigal, Iterative Solution of Linear Systems, Acta Numerica 1, pp. 1–44, 1992

    Google Scholar 

  6. A. Greenbaum. M. Rozložník, Z. Strakoš, Numerical Behaviour of the Modified Gram Schmidt GMRES Method, (submitted to BIT)

    Google Scholar 

  7. Y. Saad, M.H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM J. Sci. Stat. Comput. 7, pp. 856–869, 1986

    Google Scholar 

  8. H. F. Walker, Implementation of the GMRES method using Householder transformations, SIAM J. Sci. Stat. Comput. 9, 1 (1988), pp. 152–163.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 2, 182 07, Praha 8, Czech Republic

    M. Rozložník, Z. Strakoš & M. Tůma

Authors
  1. M. Rozložník
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  2. Z. Strakoš
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  3. M. Tůma
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Editor information

Keith G. Jeffery Jaroslav Král Miroslav Bartošek

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© 1996 Springer-Verlag Berlin Heidelberg

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Rozložník, M., Strakoš, Z., Tůma, M. (1996). On the role of orthogonality in the GMRES method. In: Jeffery, K.G., Král, J., Bartošek, M. (eds) SOFSEM'96: Theory and Practice of Informatics. SOFSEM 1996. Lecture Notes in Computer Science, vol 1175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037424

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  • DOI: https://doi.org/10.1007/BFb0037424

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61994-9

  • Online ISBN: 978-3-540-49588-8

  • eBook Packages: Springer Book Archive

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