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| Two Minimal Residual NHSS Iteration Methods for Complex Symmetric Linear Systems |
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| KeyWord:Complex symmetric linear systems, minimal residual technique, inexact versions, convergence properties |
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| Abstract: |
| For the large sparse complex symmetric linear systems, by applying the minimal residual technique to accelerate a preconditioned variant of new Hermitian and skew-Hermitian splitting (P$^*$NHSS) method and efficient parameterized P$^*$NHSS (PPNHSS) method, we construct the minimal residual P$^*$NHSS (MRP$^*$NHSS) method and the minimal residual PPNHSS (MRPPNHSS) method. The convergence properties of the two iteration methods are studied. Theoretical analyses imply that the MRP$^*$NHSS method and the MRPPNHSS method converge unconditionally to the unique solution. In addition, we also give the inexact versions of MRP$^*$NHSS method and MRPPNHSS method and their convergence proofs. Finally, numerical experiments show the high efficiency and robustness of our methods. |
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