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A Generalized GMRES Iterative Method

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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Abstract

We describe a generalization of the GMRES iterative method in which the residual vector is no longer minimized in the 2-norm but in a C-norm, where C is a symmetric positive definite matrix. The resulting iterative method call GGMRES is derived in detail and the minimizing property is proven.

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Author information

Authors and Affiliations

  1. University of Texas at Austin, TX 78712, Austin, USA

    David R. Kincaid & David M. Young

  2. I-Shou University, Kaohsiung 840, Ta-Hsu, Taiwan

    Jen-Yuan Chen

Authors
  1. David R. Kincaid
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  2. Jen-Yuan Chen
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  3. David M. Young
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Kincaid, D.R., Chen, JY., Young, D.M. (2001). A Generalized GMRES Iterative Method. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_55

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  • DOI: https://doi.org/10.1007/3-540-45262-1_55

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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