Elegant Iterative Methods for Solving a Nonlinear Matrix Equation X-A^* e^X A=I

Authors

  • Chacha S Chacha Department of Mathematics, Physics and Informatics, Mkwawa University College of Education P. O. Box 2513, Iringa, Tanzania.

DOI:

https://doi.org/10.4314/tjs.v47i3.14

Keywords:

Hermitian positive definite solution, nonlinear matrix equation, modified fixed point method, iterative method

Abstract

The nonlinear matrix equation   was solved by Gao (2016) via standard fixed point method. In this paper, three more elegant iterative methods are proposed to find the approximate solution of the nonlinear matrix equation  namely: Newton’s method; modified fixed point method and a combination of Newton’s method and fixed point method. The convergence of Newton’s method and modified fixed point method are derived. Comparative numerical experimental results indicate that the new developed algorithms have both less computational time and good convergence properties when compared to their respective standard algorithms.

Keywords: Hermitian positive definite solution, nonlinear matrix equation, modified fixed point method, iterative method.

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Published

31-08-2021

How to Cite

Chacha, C. S. . (2021). Elegant Iterative Methods for Solving a Nonlinear Matrix Equation X-A^* e^X A=I. Tanzania Journal of Science, 47(3), 1033–1040. https://doi.org/10.4314/tjs.v47i3.14

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Articles