New iterative procedures for approximating different types of inverse matrix: convergence and stability,
New iterative procedures for approximating different types of inverse matrix: convergence and stability,
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Date
2025-01-25
Authors
Elaine Segura
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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.
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Publicado para la revista: " Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd."
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Citation
Segura, E. (2025). New Iterative Procedures for Approximating Different Types of Inverse Matrix: Convergence and Stability. Mathematical Methods in the Applied Sciences.