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CMMSE: New iterative procedures for approximating different types of inverse matrix: convergence and stability
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  • Alicia Cordero,
  • Elaine Segura,
  • Juan Ramon Torregrosa,
  • Maria P. Vassileva
Alicia Cordero
Universitat Politecnica de Valencia Institut de Matematica Multidisciplinar
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Elaine Segura
Universidad Autonoma de Santo Domingo
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Juan Ramon Torregrosa
Universitat Politecnica de Valencia Institut de Matematica Multidisciplinar

Corresponding Author:jrtorre@mat.upv.es

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Maria P. Vassileva
Instituto Tecnologico de Santo Domingo
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Abstract

In this paper, we propose a new parametric family of iterative schemes to compute the inverse of a complex nonsingular matrix. It is shown that the members of this family have at least a fourth-order of convergence. A particular element of the class is extended to approximate the Moore-Penrose inverse of rectangular complex matrices, keeping the convergence order. A dynamic analysis is performed to obtain a parameter domain in which stability is assured and to detect which members of the proposed family have good stability properties and which have chaotic behavior. Some numerical examples, with matrices of different sizes, are tested to confirm the theoretical and dynamical results.
09 Sep 2024Submitted to Mathematical Methods in the Applied Sciences
09 Sep 2024Submission Checks Completed
09 Sep 2024Assigned to Editor
10 Sep 2024Review(s) Completed, Editorial Evaluation Pending
12 Sep 2024Reviewer(s) Assigned