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Study on the GMRES (m) Method of Krylov Subspace and Its Application

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  • Silin Bai
  • Jianping Liu

Abstract

The Krylov subspace GMRES (m) method is the programming arithmetic based on the projection method. Now, it has become into the excellent arithmetic to solve the linear problem with large scale, and it also can be applied in the nonlinear programming problems. In this article, we translate the nonlinear optimization problems into the non-smooth equations to solve them. We put forward the iterative method of Newton-GMRES to solve the non-smooth equations, and for large-sized problem, this method is especially applied. And the samples also prove the validity of this method.

Suggested Citation

  • Silin Bai & Jianping Liu, 2008. "Study on the GMRES (m) Method of Krylov Subspace and Its Application," Modern Applied Science, Canadian Center of Science and Education, vol. 2(6), pages 124-124, November.
    • Handle: RePEc:ibn:masjnl:v:2:y:2008:i:6:p:124
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    References listed on IDEAS

    as
    1. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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