Improving Newton–Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory

Alicia Cordero (), Javier G. Maimó, Juan R. Torregrosa and María P. Vassileva
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Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 Valencia, Spain
Javier G. Maimó: Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Procéres, Gala, Santo Domingo 10602, Dominican Republic
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 Valencia, Spain
María P. Vassileva: Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Procéres, Gala, Santo Domingo 10602, Dominican Republic

Mathematics, 2023, vol. 11, issue 14, 1-19

Abstract: 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 × 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.

Keywords: nonlinear matrix equations; inverse and pseudo-inverse matrices; iterative procedure; methods with memory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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