JP Journal of Algebra, Number Theory and Applications
Volume 39, Issue 6, Pages 959 - 989
(December 2017) http://dx.doi.org/10.17654/NT039060959 |
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BACKWARD PERTURBATION ANALYSIS AND RELATIVE ALGORITHMS FOR NONSYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES
Zhanshan Yang and Xilan Liu
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Abstract: This paper presents a backward perturbation analysis of a block Krylov subspace method for the solution of nonsymmetric linear systems GMin-Pet algorithm is given which minimizes the block joint backward perturbation norm of the matrix and computes an approximate solution satisfying at each step. For the benefit of the amount of calculation, we give lower and upper bounds about that is easier to compute. The block minimum perturbation algorithm is used to analyze the performance of these block Krylov subspace methods by evaluating the proximity of their solutions to block joint backward perturbation optimality. |
Keywords and phrases: backward perturbation, Kronecker product, minimum joint backward perturbation, global Arnoldi, matrix Krylov subspace, block methods, iterative methods, nonsymmetric linear systems, multiple right-hand sides. |
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