Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations
Chacha Stephen Chacha, Hyun-Min Kim · East Asian Journal on Applied Mathematics · 2019
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, $n$ > 2are 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.