On the preconditioning of matrices with skew-symmetric splittings

The rates of convergence of iterative methods with standard preconditioning techniques usually degrade when the skew-symmetric part S of the matrix is relatively large. In this paper, we address the issue of preconditioning matrices with such large skew-symmetric parts. The main idea of the preconditioner is to split the matrix into its symmetric and skew-symmetric parts and to “invert” the (shifted) skew-symmetric matrix. Successful use of the method requires the solution of a linear system with matrix I+S. An efficient method is developed using the normal equations, preconditioned by an incomplete orthogonal factorization.