Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations
type: Item
instance of: scholarly article
title: Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations
zbMATH Open document ID: 1169.65038
author: J. Martínez
published in: Linear Algebra and its Applications
publication date: 2009-02-25T00:00:00Z
review text: The authors present structured doubling algorithms for the computation of the weakly stabilizing Hermitian solutions of the continuous- and discrete-time algebraic Riccati equations (CARE and DARE), respectively. It is assumed that the partial multiplicities of purely imaginary and unimodular eigenvalues of the associated Hamiltomian and symplectic pencil, respectively, are all even and the C/DARE and the dual C/DARE have weakly stabilizing Hermitian solutions with property (P). Under these assumptions, it is proved that if the algorithms do not break down, they converge to the desired Hermitian solutions globally and linearly. The effectiveness of the algorithms is tested with some numerical experiments.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 5518762
zbMATH Keywords: algebraic Riccati equation
zbMATH Keywords: Hermitian solution
zbMATH Keywords: structured doubling algorithm
zbMATH Keywords: purely imaginary eigenvalue
zbMATH Keywords: unimodular eigenvalue
zbMATH Keywords: global and linear convergence
zbMATH Keywords: Hamiltonian and symplectic pencil
zbMATH Keywords: algorithms
zbMATH Keywords: numerical experiments
reviewed by: Sonia Pérez Díaz
describes a project that uses: HQR3 EXCHNG
describes a project that uses: Matlab
describes a project that uses: mctoolbox
describes a project that uses: HQR3
MaRDI profile type: Publication
full work available at URL: j.laa.2007.08.043
OpenAlex ID: W2122055952
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DOI: 10.1016/J.LAA.2007.08.043
description: scientific article; zbMATH DE number 5518762