Minimal Residual Methods for Complex Symmetric, Skew Symmetric, and Skew Hermitian Systems
|Title||Minimal Residual Methods for Complex Symmetric, Skew Symmetric, and Skew Hermitian Systems|
|Year of Publication||2012|
While there is no lack of efficient Krylov subspace solvers for Hermitian systems, there are few for complex symmetric, skew symmetric, or skew Hermitian systems, which are increasingly important in modern applications including quantum dynamics, electromagnetics, and power systems. For a large consistent complex symmetric system, one may apply a non-Hermitian Krylov subspace method disregarding the symmetry of A, or a Hermitian Krylov solver on the equivalent normal equation or an augmented system twice the original dimension. These have the disadvantages of increasing either memory, conditioning, or computational costs. An exception is a special version of QMR by Freund (1992), but that may be affected by non-benign breakdowns unless look-ahead is implemented; furthermore, it is designed for only consistent and nonsingular problems. For skew symmetric systems, Greif and Varah (2009) adapted CG for nonsingular skew symmetric linear systems that are necessarily and restrictively of even order.