On symmetric block triangular splitting iteration method for a class of complex symmetric system of linear equations |
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Institution: | 1. The 20th Institute of China Electronics Technology Group Corporation, Shanxi Province, Xi’an 710068, PR China;2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China;3. Key Laboratory of Applied Mathematics and Complex Systems, Gansu Province, Lanzhou 730000, PR China |
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Abstract: | For solving a class of complex symmetric linear system, we first transform the system into a block two-by-two real formulation and construct a symmetric block triangular splitting (SBTS) iteration method based on two splittings. Then, eigenvalues of iterative matrix are calculated, convergence conditions with relaxation parameter are derived, and two optimal parameters are obtained. Besides, we present the optimal convergence factor and test two numerical examples to confirm theoretical results and to verify the high performances of SBTS iteration method compared with two classical methods. |
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Keywords: | Complex linear system Symmetric positive definite Block triangular Splitting Convergence |
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