Inversion–free Iterative Method for Finding Symmetric Solution of the Nonlinear Matrix Equation X-A^* X^q A=I (q≥2)

Authors

Chacha Stephen Chacha, Department of Mathematics, Physics and Informatics, Mkwawa University College of Education, University of Dar es Salaam, P. O. Box 2513, Iringa, TanzaniaFollow

Section

Physical Sciences

Abstract

In this paper, we propose the inversion free iterative method to find symmetric solution of the nonlinear matrix equation  where  is an unknown symmetric solution,  is a given Hermitian matrix and  is a positive integer. The convergence of the proposed method is derived. Numerical examples demonstrate that the proposed iterative method is quite efficient and converges well when the initial guess is sufficiently close to the approximate solution. Keywords: Symmetric solution, nonlinear matrix equation, inversion free, iterative method.

Recommended Citation

Chacha, Chacha Stephen (2021) "Inversion–free Iterative Method for Finding Symmetric Solution of the Nonlinear Matrix Equation X-A^* X^q A=I (q≥2)," Tanzania Journal of Science: Vol. 47: Iss. 4, Article 13.
Available at:https://doi.org/10.4314/tjs.v47i4.5