Practical Use of Some Krylov Subspace Methods for Solving Indefinite and Nonsymmetric Linear Systems

1984 ◽  
Vol 5 (1) ◽  
pp. 203-228 ◽  
Author(s):  
Youcef Saad
Keyword(s):  
Linear Systems ◽  
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.

scholarly journals Krylov Subspace Methods for Linear Systems with Tensor Product Structure

2010 ◽  
Vol 31 (4) ◽  
pp. 1688-1714 ◽  
Author(s):  
Daniel Kressner ◽  
Christine Tobler
Keyword(s):  
Tensor Product ◽  
Linear Systems ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Product Structure ◽  
Subspace Methods
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