Block minimum perturbation algorithm based on block Arnoldi process for nonsymmetric linear systems with multiple right-hand sides

2019 ◽  
Vol 347 ◽  
pp. 741-766
Author(s):  
Zhanshan Yang ◽  
Bing Zheng
Keyword(s):  
Linear Systems ◽  
Arnoldi Process ◽  
Nonsymmetric Linear Systems ◽  
Right Hand ◽  
Block Arnoldi

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.

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
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