Preconditioning of GMRES by skew-Hermitian iterations

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• 作者：L. A. Krukier ; T. S. Martynova
• 关键词：Hermitian and skew ; Hermitian splitting ; iterative methods ; preconditioning ; Krylov subspace methods ; saddle point linear system
• 刊名：Numerical Analysis and Applications
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：9
• 期：3
• 页码：207-217
• 全文大小：622 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1995-4247
• 卷排序：9

文摘

A class of preconditioners for solving non-Hermitian positive definite systems of linear algebraic equations is proposed and investigated. It is based on Hermitian and skew-Hermitian splitting of the initial matrix. A generalization for saddle point systems having semidefinite or singular (1, 1) blocks is given. Our approach is based on an augmented Lagrangian formulation. It is shown that such preconditioners can be efficiently used for the iterative solution of systems of linear algebraic equations by the GMRES method.