## CGS, a fast Lanczos-type solver for nonsymmetric linear systems.(English)Zbl 0666.65029

The presented method is a combination of the CGS algorithm (a “squared” conjugate gradient method) with a preconditioning called ILLU (an incomplete line-LU-factorization). The conclusion of the author is that this combination is a competitive solver for nonsymmetric linear systems, at least for problems that are not too large, and when high accuracy is required. Numerical experiments show that the average work for solving convection-diffusion equations in two dimensions is roughly $$O(N^{3/2})$$.
Reviewer: G.Maeß

### MSC:

 65F10 Iterative numerical methods for linear systems 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs

CGS; BiCGstab
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