Volume 23, Issue 3
On the Minimal Nonnegative Solution of Nonsymmetric Algebraic Riccati Equation
DOI:

J. Comp. Math., 23 (2005), pp. 305-320

Published online: 2005-06

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• Abstract

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.

• Keywords

Nonsymmetric algebraic Riccati equation Minimal nonnegative solution Matrix sign function Quadratic matrix equation

@Article{JCM-23-305, author = {}, title = {On the Minimal Nonnegative Solution of Nonsymmetric Algebraic Riccati Equation}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {3}, pages = {305--320}, abstract = { 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8817.html} }
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://dor.org/ UR - https://global-sci.org/intro/jcm/8817.html KW - Nonsymmetric algebraic Riccati equation KW - Minimal nonnegative solution KW - Matrix sign function KW - 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.