scholarly journals A Multilevel Cholesky Conjugate Gradients Hybrid Solver for Linear Systems with Multiple Right-hand Sides

2011 ◽  
Vol 4 ◽  
pp. 2307-2316 ◽  
Author(s):  
Joshua Dennis Booth ◽  
Anirban Chatterjee ◽  
Padma Raghavan ◽  
Michael Frasca
Keyword(s):  
Linear Systems ◽  
Conjugate Gradients ◽  
Right Hand ◽  
Hybrid Solver

scholarly journals A block GMRES method with deflated restarting for solving linear systems with multiple shifts and multiple right-hand sides

2018 ◽  
Vol 25 (5) ◽  
pp. e2148 ◽  
Author(s):  
Dong-Lin Sun ◽  
Ting-Zhu Huang ◽  
Yan-Fei Jing ◽  
Bruno Carpentieri
Keyword(s):  
Linear Systems ◽  
Gmres Method ◽  
Right Hand ◽  
Deflated Restarting

scholarly journals A Polynomial Preconditioned Global CMRH Method for Linear Systems with Multiple Right-Hand Sides

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ke Zhang ◽  
Chuanqing Gu
Keyword(s):  
Theoretical Result ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Polynomial Degree ◽  
Right Hand

The restarted global CMRH method (Gl-CMRH(m)) (Heyouni, 2001) is an attractive method for linear systems with multiple right-hand sides. However, Gl-CMRH(m) may converge slowly or even stagnate due to a limited Krylov subspace. To ameliorate this drawback, a polynomial preconditioned variant of Gl-CMRH(m) is presented. We give a theoretical result for the square case that assures that the number of restarts can be reduced with increasing values of the polynomial degree. Numerical experiments from real applications are used to validate the effectiveness of the proposed method.

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