Real valued iterative methods for solving complex symmetric linear systems

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 prec onditioned matrix is bounded above by 2, so only very few iterations an req uired. Applications when solving matrix polynomial equation systems, linear systems of ordinary differential equations, and using time-stepping integr ation schemes based on Pade approximation for parabolic and hyperbolic prob lems are also discussed. Numerical comparisons show that the proposed real valued method is much faster than the iterative complex symmetric QMR metho d. Copyright (C) 2000 John Wiley & Sons, Ltd.