A parameterized splitting iteration method for complex symmetric linear systems. (English) Zbl 1307.65038

The paper introduces and tests a parametrized splitting method (PS) to solve complex symmetric systems \((W + iT)x = b \in \mathbb C^n\) with positive (semi-)definite real symmetric matrices \(W\) and \(T\). The spectral radius of the iteration matrix is explicitly computed in terms of specific Raleigh quotients for \(W\) and \(TW^{-1}T\). This allows finding the optimal iteration parameter in terms of the extreme real eigenvalues of \(W\) and \(TW^{-1}T\). The PS method is further sped up by using preconditioned Krylov methods and restarts. Various such preconditioners are tested in conjunction with PS and give excellent results for sparse complex symmetric systems.


65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
65F08 Preconditioners for iterative methods
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
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