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...

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Detalles Bibliográficos
Autores: Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761, Maimo, Javier G., Vassileva, María P.
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
Descripción
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.