Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Krylov subspace methods for solving large unsymmetric linear systems

Author: Y. Saad
Journal: Math. Comp. 37 (1981), 105-126
MSC: Primary 65F10
MathSciNet review: 616364
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Some algorithms based upon a projection process onto the Krylov subspace ${K_m} = \operatorname {Span}({r_0},A{r_0}, \ldots ,{A^{m - 1}}{r_0})$ are developed, generalizing the method of Conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldi’s algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace ${K_m}$ and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F10

Retrieve articles in all journals with MSC: 65F10

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society