GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. (English) Zbl 0599.65018

Saad, Youcef; Schultz, Martin H.

SIAM J. Sci. Stat. Comput. 7, 856-869 (1986).

An iterative algorithm for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace is presented. The new method presents several advantages over the ”generalized conjugate residual” method and the ORTHODIR method. Few numerical comparisons are given.

Reviewer: S.Filippi

MSC:

65F10	Iterative numerical methods for linear systems
65F25	Orthogonalization in numerical linear algebra

Keywords:

minimal residual method; generalized conjugate residual method; iterative algorithm; Krylov subspace; ORTHODIR method; numerical comparisons