A comparison of iterative methods to solve complex valued linear algebraic systems (Q403093): Difference between revisions

This overview and analysis of various iterative methods to solve sparse complex linear equations includes both preconditioning and splitting methods as well as extensive and detailed tests and numerical experiments. In general, it is advisable to replace a sparse complex linear system \(Cz = h \in \mathbb C^n\) by a \(2n\) by \(2n\) real system such as \( \begin{bmatrix} A & -B\\B & A \end{bmatrix} \begin{pmatrix} x\\y \end{pmatrix} = \begin{pmatrix} f\\g \end{pmatrix}\) or \( \begin{bmatrix} B & -A\\A & B \end{bmatrix} \begin{pmatrix} x\\-y \end{pmatrix} = \begin{pmatrix} g\\f \end{pmatrix}\) where \(C = A + iB, \;z = x+iy\) and \(h = f+ig\) and all right hand entries in the last three equations are real, except for \(i = \sqrt{-1}\). The advice in the conclusions section should be heeded by anyone in need solving complex sparse linear systems.