Abstract
Preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) method is an unconditionally convergent iteration method for solving large sparse complex symmetric systems of linear equation. Motivated by the PMHSS method, we develop a new method of solving a class of linear equations with block two-by-two complex coefficient matrix by introducing two coefficients, noted as DPMHSS. By making use of the DPMHH iteration as the inner solver to approximately solve the Newton equations, we establish modified Newton-DPMHSS (MN-DPMHSS) method for solving large systems of nonlinear equations. We analyze the local convergence properties under the Hölder continuous conditions, which is weaker than Lipschitz assumptions. Numerical results are given to confirm the effectiveness of our method.
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The authors are very much indebted to the referees for their constructive and valuable comments and suggestions which greatly improved the original version of this paper.
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Xue-Ping Guo is partly supported by the National Natural Science Foundation of China (No.11371145, No.11471122), Science and Technology Commission of Shanghai Municipality (STCSM, 13dz2260400).
Hong-Xiu Zhong is partly supported by the National Natural Science Foundation of China (No. 11471122).
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Wang, J., Guo, XP. & Zhong, HX. MN-DPMHSS iteration method for systems of nonlinear equations with block two-by-two complex Jacobian matrices. Numer Algor 77, 167–184 (2018). https://doi.org/10.1007/s11075-017-0309-x
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DOI: https://doi.org/10.1007/s11075-017-0309-x