Generalized Inverses Estimations by Means of Iterative Methods with Memory

Santiago Artidiello, Alicia Cordero, Juan R. Torregrosa and María P. Vassileva
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Santiago Artidiello: Instituto Tecnológico de Santo Domingo (INTEC), 10602 Santo Domingo, Dominican Republic
Alicia Cordero: Multidisciplinary Institute of Mathematics, Universitat Politècnica de València, 46022 València, Spain
Juan R. Torregrosa: Multidisciplinary Institute of Mathematics, Universitat Politècnica de València, 46022 València, Spain
María P. Vassileva: Instituto Tecnológico de Santo Domingo (INTEC), 10602 Santo Domingo, Dominican Republic

Mathematics, 2019, vol. 8, issue 1, 1-13

Abstract: A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A . For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an approximation of the Moore–Penrose inverse and Drazin inverse are obtained. The convergence and the order of convergence is presented in each case. Some numerical tests allowed us to confirm the theoretical results and to compare the performance of our method with other known ones. With these results, the iterative methods with memory appear for the first time for estimating the solution of a nonlinear matrix equations.

Keywords: nonlinear matrix equation; iterative method; secant method; convergence; singular value decomposition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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