Modified Newton-NSS method for solving systems of nonlinear equations
| Autor: | Qingbiao Wu, Min-Hong Chen, Ping-Fei Dai |
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| Rok vydání: | 2017 |
| Předmět: |
Iterative method
Astrophysics::High Energy Astrophysical Phenomena Applied Mathematics Numerical analysis Mathematical analysis 010103 numerical & computational mathematics Solver 01 natural sciences Local convergence 010101 applied mathematics symbols.namesake Nonlinear system Rate of convergence Jacobian matrix and determinant symbols 0101 mathematics Newton's method Mathematics |
| Zdroj: | Numerical Algorithms. 77:1-21 |
| ISSN: | 1572-9265 1017-1398 |
| DOI: | 10.1007/s11075-017-0301-5 |
| Popis: | By making use of the normal and skew-Hermitian splitting (NSS) method as the inner solver for the modified Newton method, we establish a class of modified Newton-NSS method for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. Under proper conditions, the local convergence theorem is proved. Furthermore, the successive-overrelaxation (SOR) technique has been proved quite successfully in accelerating the convergence rate of the NSS or the Hermitian and skew-Hermitian splitting (HSS) iteration method, so we employ the SOR method in the NSS iteration, and we get a new method, which is called modified Newton SNSS method. Numerical results are given to examine its feasibility and effectiveness. |
| Databáze: | OpenAIRE |
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