BACKWARD PERTURBATION ANALYSIS AND RELATIVE ALGORITHMS FOR NONSYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES

2017 ◽  
Vol 39 (6) ◽  
pp. 959-989
Author(s):  
Zhanshan Yang ◽  
Xilan Liu
Keyword(s):  
Linear Systems ◽  
Perturbation Analysis ◽  
Nonsymmetric Linear Systems ◽  
Right Hand ◽  
Backward Perturbation

scholarly journals A block IDR(s) method for nonsymmetric linear systems with multiple right-hand sides

2011 ◽  
Vol 235 (14) ◽  
pp. 4095-4106 ◽  
Author(s):  
L. Du ◽  
T. Sogabe ◽  
B. Yu ◽  
Y. Yamamoto ◽  
S.-L. Zhang
Keyword(s):  
Linear Systems ◽  
Nonsymmetric Linear Systems ◽  
Right Hand

scholarly journals Optimal Backward Perturbation Analysis for the Block Skew Circulant Linear Systems with Skew Circulant Blocks

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhaolin Jiang ◽  
Juan Li ◽  
Jianwei Zhou
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Perturbation Analysis ◽  
Spectral Decomposition ◽  
Circulant Matrix ◽  
Singular Value ◽  
Backward Perturbation ◽  
Skew Circulant

We first give the block style spectral decomposition of arbitrary block skew circulant matrix with skew circulant blocks. Secondly, we obtain the singular value of block skew circulant matrix with skew circulant blocks as well. Finally, based on the block style spectral decomposition, we deal with the optimal backward perturbation analysis for the block skew circulant linear system with skew circulant blocks.

scholarly journals Residual-Based Simpler Block GMRES for Nonsymmetric Linear Systems with Multiple Right-Hand Sides

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Qinghua Wu ◽  
Liang Bao ◽  
Yiqin Lin
Keyword(s):  
Linear Systems ◽  
Linear Dependence ◽  
Numerical Experiments ◽  
Gmres Method ◽  
Algebraic Equations ◽  
Rank Deficiency ◽  
Nonsymmetric Linear Systems ◽  
Right Hand ◽  
Linear Algebraic Equations ◽  
Block Arnoldi

We propose in this paper a residual-based simpler block GMRES method for solving a system of linear algebraic equations with multiple right-hand sides. We show that this method is mathematically equivalent to the block GMRES method and thus equivalent to the simpler block GMRES method. Moreover, it is shown that the residual-based method is numerically more stable than the simpler block GMRES method. Based on the deflation strategy proposed by Calandra et al. (2013), we derive a deflation strategy to detect the possible linear dependence of the residuals and a near rank deficiency occurring in the block Arnoldi procedure. Numerical experiments are conducted to illustrate the performance of the new method.

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