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.
Reviewer: Frank Uhlig (Auburn)
MSC:
| 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.) |
Keywords:
complex symmetric linear equations; parametrized splitting iteration; spectral radius; preconditioning; sparse matrix; Raleigh quotient; Krylov methodReferences:
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