On CSCS-based iteration methods for Toeplitz system of weakly nonlinear equations |
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Authors: | Mu-Zheng Zhu Guo-Feng Zhang |
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Institution: | a School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR Chinab Department of Mathematics, Hexi University, Zhangye 734000, PR China |
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Abstract: | For Toeplitz system of weakly nonlinear equations, by using the separability and strong dominance between the linear and the nonlinear terms and using the circulant and skew-circulant splitting (CSCS) iteration technique, we establish two nonlinear composite iteration schemes, called Picard-CSCS and nonlinear CSCS-like iteration methods, respectively. The advantage of these methods is that they do not require accurate computation and storage of Jacobian matrix, and only need to solve linear sub-systems of constant coefficient matrices. Therefore, computational workloads and computer storage may be saved in actual implementations. Theoretical analysis shows that these new iteration methods are local convergent under suitable conditions. Numerical results show that both Picard-CSCS and nonlinear CSCS-like iteration methods are feasible and effective for some cases. |
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Keywords: | 65F10 65F50 65T50 65Y05 |
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