BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. (English) Zbl 0761.65023

Van der Vorst, H. A.

SIAM J. Sci. Stat. Comput. 13, No. 2, 631-644 (1992).

In order to improve the convergence properties of the conjugate gradients-squared method, the author suggests making use of preconditioned matrices. Four examples of symmetric and nonsymmetric matrices are considered where modified incomplete Cholesky decomposition or incomplete LU-factorization is used. The calculation results show that the residual in this case decreases considerably faster and that this decrease is almost monotonous.

Reviewer: Y.Shokin (Krasnoyarsk)

MSC:

65F10	Iterative numerical methods for linear systems
65F35	Numerical computation of matrix norms, conditioning, scaling

Keywords:

conjugate gradients-squared method; Bi-conjugate gradients method; numerical experiments; Bi-CGSTAB; nonsymmetric linear systems; iterative solver; preconditioning

Software:

Bi-CG