Year: 2019
Author: Chacha Stephen Chacha, Hyun-Min Kim
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 4 : pp. 665–682
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.300518.120119
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 4 : pp. 665–682
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Elementwise minimal nonnegative solution Newton’s method monotonic convergence nonlinear matrix equation.