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