scholarly journals Block Krylov Subspace Recycling for Shifted Systems with Unrelated Right-Hand Sides

2016 ◽  
Vol 38 (1) ◽  
pp. A302-A324 ◽  
Author(s):  
Kirk M. Soodhalter
Keyword(s):  
Krylov Subspace ◽  
Right Hand ◽  
Subspace Recycling

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.

scholarly journals Krylov subspace recycling for evolving structures

2022 ◽  
pp. 114222
Author(s):  
M. Bolten ◽  
E. de Sturler ◽  
C. Hahn ◽  
M.L. Parks
Keyword(s):  
Krylov Subspace ◽  
Subspace Recycling

Enlarged GMRES for solving linear systems with one or multiple right-hand sides

2018 ◽  
Vol 39 (4) ◽  
pp. 1924-1956 ◽  
Author(s):  
Hussam Al Daas ◽  
Laura Grigori ◽  
Pascal Hénon ◽  
Philippe Ricoux
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Real Life ◽  
Original Method ◽  
Gmres Method ◽  
Convection Diffusion ◽  
Right Hand ◽  
Test Matrices ◽  
Linear Systems Of Equations ◽  
Diffusion Problems

Abstract We propose a variant of the generalized minimal residual (GMRES) method for solving linear systems of equations with one or multiple right-hand sides. Our method is based on the idea of the enlarged Krylov subspace to reduce communication. It can be interpreted as a block GMRES method. Hence, we are interested in detecting inexact breakdowns. We introduce a strategy to perform the test of detection. Furthermore, we propose a technique for deflating eigenvalues that has two benefits. The first advantage is to avoid the plateau of convergence after the end of a cycle in the restarted version. The second is to have very fast convergence when solving the same system with different right-hand sides, each given at a different time (useful in the context of a constrained pressure residual preconditioner). We test our method with these deflation techniques on academic test matrices arising from solving linear elasticity and convection–diffusion problems as well as matrices arising from two real-life applications, seismic imaging and simulations of reservoirs. With the same memory cost we obtain a saving of up to $50 \%$ in the number of iterations required to reach convergence with respect to the original method.

Multisplitting for regularized least squares with Krylov subspace recycling

2011 ◽  
Vol 19 (4) ◽  
pp. 655-676 ◽  
Author(s):  
Rosemary A. Renaut ◽  
Youzuo Lin ◽  
Hongbin Guo
Keyword(s):  
Least Squares ◽  
Krylov Subspace ◽  
Regularized Least Squares ◽  
Subspace Recycling

scholarly journals Krylov subspace recycling for sequences of shifted linear systems

2014 ◽  
Vol 81 ◽  
pp. 105-118 ◽  
Author(s):  
Kirk M. Soodhalter ◽  
Daniel B. Szyld ◽  
Fei Xue
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Shifted Linear Systems ◽  
Subspace Recycling
Sign in / Sign up

Export Citation Format

Share Document