PROJECTION-ITERATION REALIZATION OF A NEWTON-LIKE METHOD FOR SOLVING NONLINEAR OPERATOR EQUATIONS
We consider the problem of existence and location of a solution of a nonlinear operator equation with a Fr´echet differentiable operator in a Banach space and present the convergence results for a projection-iteration method based on a Newton-like method under the Cauchy’s conditions, which generali...
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2019-03-01
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| Series: | Journal of Optimization, Differential Equations and Their Applications |
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| Online Access: | https://model-dnu.dp.ua/index.php/SM/article/view/134 |
| Summary: | We consider the problem of existence and location of a solution of a nonlinear
operator equation with a Fr´echet differentiable operator in a Banach space and present the convergence results for a projection-iteration method based on a Newton-like method under the Cauchy’s conditions, which generalize the results for the projection-iteration realization of the Newton-Kantorovich method. The proposed method unlike the traditional interpretation is based on the idea of whatever approximation of the original equation by a sequence of approximate operator equations defined on subspaces of the basic space with the subsequent application of the Newton-like method to their approximate solution. We prove the convergence theorem, obtain the error estimate and discuss the advantages of the proposed approach and some of its modifications. |
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| ISSN: | 2617-0108 2663-6824 |