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Volume 9, Issue 4
Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations

Chacha Stephen Chacha & Hyun-Min Kim

DOI: 10.4208/eajam.300518.120119

East Asian J. Appl. Math., 9 (2019), pp. 665-682.

Published online: 2019-10

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  • 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.

  • Keywords

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

  • AMS Subject Headings

15A24, 65F30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

chchstephen@yahoo.com (Chacha Stephen Chacha)

hyunmin@pusan.ac.kr (Hyun-Min Kim)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-9-665, author = {Stephen Chacha , Chacha and Kim , Hyun-Min}, title = {Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.300518.120119}, url = {http://global-sci.org/intro/article_detail/eajam/13326.html} }
TY - JOUR T1 - Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations AU - Stephen Chacha , Chacha AU - Kim , Hyun-Min JO - East Asian Journal on Applied Mathematics VL - 4 SP - 665 EP - 682 PY - 2019 DA - 2019/10 SN - 9 DO - http://doi.org/10.4208/eajam.300518.120119 UR - https://global-sci.org/intro/article_detail/eajam/13326.html KW - Elementwise minimal nonnegative solution, Newton’s method, monotonic convergence, nonlinear matrix equation. AB -

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.

Stephen Chacha , Chacha and Kim , Hyun-Min. (2019). Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations. East Asian Journal on Applied Mathematics. 9 (4). 665-682. doi:10.4208/eajam.300518.120119
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