On the Preconditioning of Matrices with a Dominant Skew-symmetric Component

The rates of convergence of iterative methods with standard preconditioning techniques such as ILUT 9] usually degrade when the skew-symmetric component S of the matrix is relatively large. In this paper, we address the issue of preconditioning matrices with such large skew-symmetric component. The main idea of the preconditioner is to split the matrix in its symmetric and skew-symmetric part and to \invert" the (shifted) skew-symmetric matrix. Successful use of the method requires the solution of linear systems with matrix I + S. An eecient method is developed using the normal equations, preconditioned by an incomplete orthogonal factorization. Numerical experiments on various systems arising in physics show that the reduction in terms of iteration count largely compensate the additional work per iteration when compared to standard preconditioners. Also, the preconditioner still produces fast convergence for problems where ILUT breaks down because of a very large skew-symmetric component relative to the hermitian component.