Abstract
In this study, an efficient iterative method is given to solve large sparse nonlinear systems with block two-by-two complex symmetric Jacobian matrices. Based on the double-parameter preconditioned MHSS (DPMHSS) method, a modified double-parameter preconditioned MHSS (MDPMHSS) method is developed to solve a class of linear systems with block two-by-two complex coefficient matrices. Then, a modified Newton-MDPMHSS method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices is obtained, which MDPMHSS is employed as the inner iteration and the modified Newton method is employed as the outer iteration. Local convergence analysis is given for the new present method under Hölder condition, which is weaker than Lipschitz condition. At last, numerical results are reported to verify the efficiency of the new method.
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Funding
This work is supported by National Natural Science Foundation of China (Grant No. 11771393, 11632015, 11671009), Zhejiang Natural Science Foundation (Grant No. LQ18A010008, LZ14A010002), NSAF of China (Grant No. U1630116), and Science Foundation of Zhejiang Sci-Tech University (ZSTU) (Grant No. 11432932611468).
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Chen, MH., Wu, QB. Modified Newton-MDPMHSS method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices. Numer Algor 80, 355–375 (2019). https://doi.org/10.1007/s11075-018-0488-0
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DOI: https://doi.org/10.1007/s11075-018-0488-0
Keywords
- Splitting iteration
- Modified Newton-MDPMHSS method
- Large sparse nonlinear system
- Block two-by-two complex symmetric matrices
- Local convergence analysis