Solving the algebraic Riccati equation with the matrix sign function
type: Item
instance of: scholarly article
title: Solving the algebraic Riccati equation with the matrix sign function
zbMATH Open document ID: 0611.65027
DOI: 10.1016/0024-3795(87)90222-9
author: Ralph Byers
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The algebraic Riccati equation \(G+A^ TX+XA-XFX=0\) is reduced to a linear matrix equation of the form \(MX=N\) where the matrices M and N are defined by the sign function, Sign(K), of the Hamiltonian matrix \(K=\left[ \begin{matrix} A^ T\quad G\\ F\quad -A\end{matrix} \right]\). An iterative refinement of the matrix-sign-function algorithm and a stopping criterion limiting the effects of rounding errors lead to a stable numerical procedure which compares favorably with current Schur vector- based algorithms [\textit{A. Laub}, IEEE Trans. Autom. Control AC-24, 913- 921 (1979; Zbl 0424.65013)]. Comparative numerical experiments on three examples are also presented.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 3988615
zbMATH Keywords: numerical examples
zbMATH Keywords: comparison of methods
zbMATH Keywords: algebraic Riccati equation
zbMATH Keywords: linear matrix equation
zbMATH Keywords: Hamiltonian matrix
zbMATH Keywords: iterative refinement
zbMATH Keywords: stopping criterion
zbMATH Keywords: rounding errors
zbMATH Keywords: Schur vector-based algorithms
reviewed by: Ştefan Mirică
describes a project that uses: LINPACK
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90222-9
OpenAlex ID: W2077760421
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description: scientific article; zbMATH DE number 3988615