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A Block Diagonal Preconditioner for Generalised Saddle Point Problems

Part of:Basic linear algebraNumerical linear algebraNonlinear algebraic or transcendental equations

Published online by Cambridge University Press:  20 July 2016

Zhong Zheng and
Guo Feng Zhang
Zhong Zheng*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
Guo Feng Zhang*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
*
Corresponding author. Email addresses:zhengzh13@lzu.edu.cn (Z. Zheng), gf_zhang@lzu.edu.cn (G. F. Zhang)
Corresponding author. Email addresses:zhengzh13@lzu.edu.cn (Z. Zheng), gf_zhang@lzu.edu.cn (G. F. Zhang)

Abstract

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A lopsided alternating direction iteration (LADI) method and an induced block diagonal preconditioner for solving block two-by-two generalised saddle point problems are presented. The convergence of the LADI method is analysed, and the block diagonal preconditioner can accelerate the convergence rates of Krylov subspace iteration methods such as GMRES. Our new preconditioned method only requires a solver for two linear equation sub-systems with symmetric and positive definite coefficient matrices. Numerical experiments show that the GMRES with the new preconditioner is quite effective.

Keywords

Generalised saddle point problemKrylov subspace methodsalternating direction iterationpreconditioningconvergence

MSC classification

Secondary:15A06: Linear equations65F10: Iterative methods for linear systems65H10: Systems of equations

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 3 , August 2016, pp. 235 - 252
Copyright
Copyright © Global-Science Press 2016 

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