TY - JOUR T1 - On the Minimal Nonnegative Solution of Nonsymmetric Algebraic Riccati Equation 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 -

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.