ON SKEW-SYMMETRICAL PRECONDITIONING FOR STRONGLY NONSYMMETRICAL LINEAR-SYSTEMS

To solve iteratively linear system Au = b with large sparse strongly n on-symmetric matrix A we propose preconditioning <A(u)over cap> = (b) over cap, (A) over cap = (I + tau L(1))(-1)A(I + tau U-1)(-1), tau > 0 where respectively lower and upper triangular matrices L(1) and U-1 a re so that L(1) + U-1 = 1/2(A - A). Such preconditioning technique ma y be treated as a variant of ILU-factorization, and we call it MSSILU - MODIFIED SKEW-SYMMETRIC ILU. We investigate and optimize (with respe ct to tau) convergence of preconditioned Richardson method (RM) of the following special form: <(x)over cap (m + 1)> = <(I - tau(A)over cap> <(x)over cap m> + <tau(b)over cap>, m greater than or equal to 0, wher e tau is the same as in (A) over cap. for this method we give an estim ate for rate of convergence in relevant Euclidean norm for the case of positive real matrix A. Numerical experiments have included solving l inear systems arising from 5-point FD approximation of convection-diff usion equation with dominated convection by MSSILU + RM, MSSILU + GMRE S(2) and MSSILU + GMRES(10).