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

Chacha Stephen Chacha and Hyun-Min Kim

10.4208/eajam.300518.120119

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

Preview Full PDF BiBTex 6 162
  • Abstract

The existence of elementwise minimal nonnegative solutions of the nonlinear matrix equations 
ATX2A− X + I = 0,
ATXnA− 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.

  • History

Published online: 2019-10

  • AMS Subject Headings

15A24, 65F30

  • Cited by