TITLE:
Positive Definite Solutions for the System of Nonlinear Matrix Equations X + A*Y-nA = I, Y + B*X-mB = I
AUTHORS:
Salah M. El-Sayed, Asmaa M. Al-Dubiban
KEYWORDS:
System of Nonlinear Matrix Equations, Iterative Methods, Monotonic Sequence, Positive Definite Matrices
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.13,
July
15,
2014
ABSTRACT: In this paper, some properties of the positive
definite solutions for the nonlinear system of matrix equations X + A*Y-nA = I, Y + B*X-mB = I are
derived. As a matter of fact, an effective iterative method to obtain the
positive definite solutions of the system is established. These solutions are based
on the convergence of monotone sequences of positive definite matrices.
Moreover, the necessary and sufficient conditions for the existence of the
positive definite solutions are obtained. Finally, some numerical results are
given.