Topics in matrix analysis
Iterative solution methods
Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Best Approximate Solution of Matrix Equation AXB+CYD=E
SIAM Journal on Matrix Analysis and Applications
Gradient based iterative solutions for general linear matrix equations
Computers & Mathematics with Applications
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In this paper, we present a nested splitting conjugate gradient (NSCG) iteration method for solving a class of matrix equations with nonsymmetric coefficient matrices. This method is actually inner/outer iterations, which employs a CG-like method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergent and symmetric positive definite splitting of the coefficient matrices. Convergence conditions of this method are studied in depth and numerical experiments show the efficiency of this method. Moreover, we show that the use of the quasi-Hermitian splitting as a preconditioner can induce an accurate, robust and effective preconditioned Krylov subspace method.