Convergence of General Nonstationary Iterative Methods for Solving Singular Linear Equations

Authors:
Xinghua Shi;Yimin Wei;Wen Zhang
Affiliations:
10110180031@fudan.edu.cn and 09110180025@fudan.edu.cn;ymwei@fudan.edu.cnand yimin.wei@gmail.com;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2011

Citing 13
Cited 2

Topics in matrix analysis

Topics in matrix analysis
Projection methods solving rectangular systems of linear equations

Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
On the solution of singular linear systems of algebraic equations by semiiterative methods

Numerische Mathematik
The convergence of linear stationary iterative processes for solving singular unstructured systems of linear equations

SIAM Review
Convergence of non-stationary parallel multisplitting methods for hermitian positive definite matrices

Mathematics of Computation
On the convergence of nonstationary iterative methods for symmetric positive (semi)definite systems

Applied Numerical Mathematics
Comparison of Convergence of General Stationary Iterative Methods for Singular Matrices

SIAM Journal on Matrix Analysis and Applications
Nonstationary Multisplittings with General Weighting Matrices

SIAM Journal on Matrix Analysis and Applications
On the convergence of iterative methods for solving singular linear systems

Journal of Computational and Applied Mathematics
On the Convergence of Iterative Methods for Semidefinite Linear Systems

SIAM Journal on Matrix Analysis and Applications
On the Convergence of General Stationary Linear Iterative Methods for Singular Linear Systems

SIAM Journal on Matrix Analysis and Applications
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)

Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Convergence of Stationary Iterative Methods for Hermitian Semidefinite Linear Systems and Applications to Schwarz Methods

SIAM Journal on Matrix Analysis and Applications

Semi-convergence analysis of Uzawa methods for singular saddle point problems

Journal of Computational and Applied Mathematics
A preconditioned GLHSS iteration method for non-Hermitian singular saddle point problems

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we analyze the convergence of the general nonstationary iterative methods for solving consistent singular linear equations (in particular, singular Hermitian positive semidefinite linear systems), and we discuss relations of general stationary results and ours. We utilize the quotient convergence to prove the convergence of the two-stage iterative algorithms for solving the consistent singular Hermitian positive semidefinite linear equations.