On the convergence of iterative methods for solving singular linear systems

摘要

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.