
Conference publicationsAbstractsXXI conferenceIWZ(k)  a new preconditioner based on WZ decompositionCMC faculty of MSU 1 pp. (accepted)Solution of large sparse linear systems is usually performed with iterative methods. Unfortunately convergence of a method may be not very fast, so we have to find some way to improve convergence. One of such methods is preconditioning. The key idea of this method is to solve an equivalent system with better spectral properties. This system is obtained by multiplying the original system by a special matrix called preconditioner. There are several ways to construct a preconditioner. One of them is to use some incomplete decomposition of the coefficient matrix. The most known of preconditioners of this type is an ILU preconditioner. This report describes construction and numerical investigation of a new preconditioner based on WZ decomposition. It's a generalization of IWZ(0) preconditioner introduced by Bylina and Bylina. Our main idea is to keep more fillin in W and Z factors. Using numerical experiments it was shown that the new preconditioner is more efficient than IWZ(0) as an accelerator for BiCG method when solving SLAEs, matrix of which have a uniformely distributed spectrum.
