Abstract
Double-step scale splitting (DSS) iteration method is proved to be an unconditionally convergent iteration method, which is also efficient and robust for solving a class of large sparse complex symmetric systems of linear equations. In this paper, by making use of the DSS iteration technique as the inner solver to approximately solve the Newton equations, we establish a new modified Newton-DSS method for solving systems of nonlinear equations whose Jacobian matrices are large, sparse, and complex symmetric. Subsequently, we investigate the local and semilocal convergence properties of our method under some proper assumptions. Finally, numerical results on some problems illustrate the superiority of our method over some previous methods.
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Funding
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11771393, 11632015), Zhejiang Natural Science Foundation (Grant No. LZ14A010002), and Science Foundation of Taizhou University (Grant No. 2017PY028).
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Xie, F., Lin, RF. & Wu, QB. Modified Newton-DSS method for solving a class of systems of nonlinear equations with complex symmetric Jacobian matrices. Numer Algor 85, 951–975 (2020). https://doi.org/10.1007/s11075-019-00847-y
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DOI: https://doi.org/10.1007/s11075-019-00847-y