scholarly journals A comparison of preconditioned Krylov subspace methods for large‐scale nonsymmetric linear systems

2018 ◽  
Vol 26 (1) ◽  
pp. e2215 ◽  
Author(s):  
Aditi Ghai ◽  
Cao Lu ◽  
Xiangmin Jiao
Keyword(s):  
Linear Systems ◽  
Large Scale ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Subspace Methods ◽  
Nonsymmetric Linear Systems

An Efficient Variant of the GMRES(m) Method Based on the Error Equations

2012 ◽  
Vol 2 (1) ◽  
pp. 19-32
Author(s):  
Akira Imakura ◽  
Tomohiro Sogabe ◽  
Shao-Liang Zhang
Keyword(s):  
Linear Systems ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Initial Guess ◽  
Subspace Methods ◽  
Nonsymmetric Linear Systems ◽  
Mathematical Background

AbstractThe GMRES(m) method proposed by Saad and Schultz is one of the most successful Krylov subspace methods for solving nonsymmetric linear systems. In this paper, we investigate how to update the initial guess to make it converge faster, and in particular propose an efficient variant of the method that exploits an unfixed update. The mathematical background of the unfixed update variant is based on the error equations, and its potential for efficient convergence is explored in some numerical experiments.

POWER GRIDS ANALYSIS IN COMPRESSED KRYLOV-SUBSPACE METHODS

2008 ◽  
Vol 17 (03) ◽  
pp. 439-446
Author(s):  
HAOHANG SU ◽  
YIMEN ZHANG ◽  
YUMING ZHANG ◽  
JINCAI MAN
Keyword(s):  
Present Method ◽  
Large Scale ◽  
Krylov Subspace ◽  
Power Grid ◽  
Excellent Result ◽  
Krylov Subspace Methods ◽  
Power Grids ◽  
Improved Method ◽  
Subspace Methods ◽  
Transient Simulations

An improved method is proposed based on compressed and Krylov-subspace iterative approaches to perform efficient static and transient simulations for large-scale power grid circuits. It is implemented with CG and BiCGStab algorithms and an excellent result has been obtained. Extensive experimental results on large-scale power grid circuits show that the present method is over 200 times faster than SPICE3 and around 10–20 times faster than ICCG method in transient simulations. Furthermore, the presented algorithm saves the memory usage over 95% of SPICE3 and 75% of ICCG method, respectively while the accuracy is not compromised.

Reduced-complexity Krylov subspace methods for large-scale MIMO channel estimation

2018 ◽  
Vol 78 ◽  
pp. 332-337 ◽  
Author(s):  
Jiayi Yang ◽  
Jun Tong ◽  
Qinghua Guo ◽  
Jiangtao Xi ◽  
Yanguang Yu
Keyword(s):  
Channel Estimation ◽  
Large Scale ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Mimo Channel ◽  
Subspace Methods ◽  
Reduced Complexity

Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations

2019 ◽  
Vol 62 (1-2) ◽  
pp. 157-177
Author(s):  
El. Mostafa Sadek ◽  
Abdeslem Hafid Bentbib ◽  
Lakhlifa Sadek ◽  
Hamad Talibi Alaoui
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Matrix Equations ◽  
Subspace Methods ◽  
Sylvester Matrix ◽  
Sylvester Matrix Equations
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