Improving Newton-Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory
[EN] Some iterative schemes with memory were designed for approximating the inverse of a nonsingular square complex matrix and the Moore-Penrose inverse of a singular square matrix or an arbitrary m x n complex matrix. A Kurchatov-type scheme and Steffensen's method with memory were develop...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/203459 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/203459 |
| Access Level: | acceso abierto |
| Palabra clave: | Nonlinear matrix equations Inverse and pseudo-inverse matrices Iterative procedure Methods with memory MATEMATICA APLICADA |
| Sumario: | [EN] Some iterative schemes with memory were designed for approximating the inverse of a nonsingular square complex matrix and the Moore-Penrose inverse of a singular square matrix or an arbitrary m x n complex matrix. A Kurchatov-type scheme and Steffensen's method with memory were developed for estimating these types of inverses, improving, in the second case, the order of convergence of the Newton-Schulz scheme. The convergence and its order were studied in the four cases, and their stability was checked as discrete dynamical systems. With large matrices, some numerical examples are presented to confirm the theoretical results and to compare the results obtained with the proposed methods with those provided by other known ones. |
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