Real valued iterative methods for solving complex symmetric linear systems

Abstract

Complex valued systems of equations with a matrix R + 1S where R and S are real valued arise in many applications. A preconditioned iterative solution method is presented when R and S are symmetric positive semi-definite and at least one of R, S is positive definite. The condition number of the preconditioned matrix is bounded above by 2, so only very few iterations are required. Applications when solving matrix polynomial equation systems, linear systems of ordinary differential equations, and using time-stepping integration schemes based on Padé approximation for parabolic and hyperbolic problems are also discussed. Numerical comparisons show that the proposed real valued method is much faster than the iterative complex symmetric QMR method. Copyright © 2000 John Wiley & Sons, Ltd.