On the convergence of iterative methods for solving singular linear systems

Authors:
Zhi-Hao Cao
Affiliations:
Department of Mathematics and Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 3
Cited 2

Multisplitting with different weighting schemes

SIAM Journal on Matrix Analysis and Applications
Multisplitting of a symmetric positive definite matrix

SIAM Journal on Matrix Analysis and Applications
Convergence of non-stationary parallel multisplitting methods for hermitian positive definite matrices

Mathematics of Computation

Convergence of General Nonstationary Iterative Methods for Solving Singular Linear Equations

SIAM Journal on Matrix Analysis and Applications
Semi-convergence analysis of Uzawa methods for singular saddle point problems

Journal of Computational and Applied Mathematics

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Abstract

In this paper, we first show that for the stationary iterative methods for solving consistent singular linear systems the convergence and the quotient convergence are equivalent. Then we use this assertion to analyze the convergence of the multisplitting algorithms for the solution of linear systems when the coefficient matrices of the linear systems are singular Hermitian positive semidefinite and the linear systems are consistent.