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This paper introduces and analyzes a preconditioned modified of the Hermitian and skew-Hermitian splitting (PMHSS). The large sparse continuous Sylvester equations are solved by PMHSS iterative algorithm based on nonHermitian, complex, positive definite/semidefinite, and symmetric matrices. We prove that the PMHSS is converged under suitable conditions. In addition, we propose an accelerated PMHSS method consisting of two preconditioned matrices and two iteration parameters {alpha}, b{eta}. Theoretical analysis showed that the convergence speed of the accelerated PMHSS is faster compared to the PMHSS. Also, the robustness and efficiency of the proposed two iterative algorithms were demonstrated in numerical experiments.
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [19] and extends those methods into a more gene
We review a family of algorithms for Lyapunov- and Riccati-type equations which are all related to each other by the idea of emph{doubling}: they construct the iterate $Q_k = X_{2^k}$ of another naturally-arising fixed-point iteration $(X_h)$ via a s
In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then apply purely o
For a linear matrix function $f$ in $X in R^{mtimes n}$ we consider inhomogeneous linear matrix equations $f(X) = E$ for $E eq 0$ that have or do not have solutions. For such systems we compute optimal norm constrained solutions iteratively using th
Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its efficiency and r