TY - JOUR
T1 - On the Minimal Nonnegative Solution of Nonsymmetric Algebraic Riccati Equation
AU - Xiao-Xia Guo & Zhong-Zhi Bai
JO - Journal of Computational Mathematics
VL - 3
SP - 305
EP - 320
PY - 2005
DA - 2005/06
SN - 23
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8817.html
KW - Nonsymmetric algebraic Riccati equation, Minimal nonnegative solution, Matrix sign function, Quadratic matrix equation.
AB - <p style="text-align: justify;">We study perturbation bound and structured condition number about the minimal nonnegative solution of nonsymmetric algebraic Riccati equation, obtaining a sharp perturbation bound and an accurate condition number. By using the matrix sign function method we present a new method for finding the minimal nonnegative solution of this algebraic Riccati equation. Based on this new method, we show how to compute the desired $M$-matrix solution of the quadratic matrix equation $X^2-EX-F=0$ by connecting it with the nonsymmetric algebraic Riccati equation, where $E$ is a diagonal matrix and $F$ is an $M$-matrix.</p>