Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices. (English) Zbl 0761.65018

Freund, Roland W.

SIAM J. Sci. Stat. Comput. 13, No. 1, 425-448 (1992).

The work employs a generalization of the non-symmetric Lanczos method based on the minimization of the residual norm. Quasiminimization implies that the minimum residual norm is sought not over the entire Krylov subspace but in some specially determined unidimensional subspace.
In the considered algorithm similarly to the standard Lanczos method the normal process of computation can break down due to the vanishing of some scalar product. Suggestions about the continuation of the iterative process in case of breakdown are given. The paper contains a considerable number of numerical results that show the advantages of the suggested method.

Reviewer: Y.Shokin (Krasnoyarsk)

MSC:

65F10	Iterative numerical methods for linear systems
65F50	Computational methods for sparse matrices
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N22	Numerical solution of discretized equations for boundary value problems involving PDEs

Keywords:

large sparse linear systems; complex Helmholtz equation; complex symmetric matrices; nonsymmetric Lanczos algorithm; biconjugate gradients; minimal residual property

Software:

CGS