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Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations

Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations
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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.

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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.

Author Details

Chacha Stephen Chacha

Hyun-Min Kim

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