Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations

Authors

  • Chacha Stephen Chacha Department of Mathematics, Mkwawa University College of Education, P.O. Box 2513, Iringa, Tanzania.
  • Hyun-Min Kim Department of Mathematics, Pusan National University, Busan, 46241, Republic of Korea.

DOI:

https://doi.org/10.4208/eajam.300518.120119

Keywords:

Elementwise minimal nonnegative solution, Newton’s method, monotonic convergence, nonlinear matrix equation.

Abstract

The existence of elementwise minimal nonnegative solutions of the nonlinear matrix equations 
                                               $A$$T$$X$2$A$ − $X$ + $I$ = 0,

                                               $A$$T$$X$$n$$A$ − $X$ + $I$ = 0, $n$ > 2

are studied. Using Newton's method with the zero initial guess, we show that under suitable conditions the corresponding iterations monotonically converge to the elementwise minimal nonnegative solutions of the above equations. Numerical experiments confirm theoretical results and the efficiency of the method.

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Published

2019-10-09

Issue

Vol. 9 No. 4 (2019)

Section

Articles