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

2012 ◽  
Vol 2 (1) ◽  
pp. 19-32
Author(s):  
Akira Imakura ◽  
Tomohiro Sogabe ◽  
Shao-Liang Zhang

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.





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