Generalizations of the Lsmr and Nscg Methods for Solving Matrix Equations
نویسنده
چکیده
In this paper, We present the generalizations of the LSMR and NSCG methods for solving matrix equations. First, based on the LSMR algorithm, the Bl-LSMR and Gl-LSMR algorithms are derived by minimizing the Frobenius norm of residual matrix of normal equation. In addition, by extending the idea of LSMR algorithm, we also present the LSMR-M algorithm for solving the general coupled matrix equations. Next, based on NSCG and NS-CGNR methods, we establish the iterative methods which are inner/outer iterations for solving the sylvester equation and matrix equation AXB = C. Convergence conditions of each method are studied in dept and by using the numerical experiments the efficiency of the methods versus some well-known iterative method are shown. We also show that the Hermitian splitting and quasi-Hermitian splitting can induce accurate, robust, and effective preconditioned Krylov subspace methods. The Extended Abstracts of The 8 Seminar on Linear Algebra and its Applications 13-14th May 2015, University of Kurdistan, Iran STRUCTURED PERTURBATIONS
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