Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search
type: Item
instance of: scholarly article
title: Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search
zbMATH Open document ID: 0949.65041
DOI: 10.1016/S0167-8191(00)00012-0
published in: Parallel Computing
publication date: 2000-08-21T00:00:00Z
review text: We investigate the numerical solution of continuous-time algebraic Riccati equations via Newton's method on serial and parallel computers with distributed memory. We apply and extend the available theory for Newton's method endowed with exact line search to accelerate convergence. We also discuss a new stopping criterion based on recent observations regarding condition and error estimates. In each iteration step of Newton's method a stable Lyapunov equation has to be solved. We propose to solve these Lyapunov equations using iterative schemes for computing the matrix sign function. This approach can be efficiently implemented on parallel computers using ScaLAPACK. Numerical experiments on an IBM sp2 multicomputer report on the accuracy, scalability, and speed-up of the implemented algorithms.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1493430
zbMATH Keywords: continuous-time algebraic Riccati equation
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: Newton's method
zbMATH Keywords: matrix sign function
zbMATH Keywords: line search
zbMATH Keywords: convergence acceleration
zbMATH Keywords: parallel computation
zbMATH Keywords: error estimates
zbMATH Keywords: numerical experiments
zbMATH Keywords: scalability
author: P. Benner
author: Ralph Byers
author: Enrique S. Quintana-Ortí
author: Gregorio Quintana-Ortí
describes a project that uses: LAPACK
describes a project that uses: PVM
describes a project that uses: KELLEY
describes a project that uses: ScaLAPACK
MaRDI profile type: Publication
full work available at URL: s0167-8191(00)00012-0
OpenAlex ID: W2041197714
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description: scientific article; zbMATH DE number 1493430