One step inversion free iterative algorithm for computing generalised bisymmetric solution for nonlinear matrix equations

Abstract

In this paper, we investigate one step inversion free iterative algorithm for computing generalised bisymmetric solution to the nonlinear matrix equations (NLME) $X+A^T{X}^{-q}A+B^T{X}^{-q}B=H(q\ge 2)$, where $A,B,H$ are given matrices, while $X$ is a generalised bisymmetric matrix to be computed. The necessary conditions for the existence of a generalised bisymmetric solution and the convergence of the suggested iterative method are derived. Some lemmas and theorems are provided and proved where the iterative solutions are obtained. Four numerical examples are presented to exhibit the effectiveness of the suggested method and to verify the theoretical findings of this paper.

KEYWORDS:

• Inversion free
• generalised bisymmetric solution
• iterative algorithm
• Newton’s method
• Frobenius norm
• nonlinear matrix equation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

Because no datasets were collected or processed during the current study, data sharing was not applicable to this paper.