Solving matrix equations on multi-core and many-core architectures
type: Item
instance of: scholarly article
title: Solving matrix equations on multi-core and many-core architectures
zbMATH Open document ID: 1461.65061
author: P. Benner
author: Pablo Ezzatti
author: Hermann Mena
author: Enrique S. Quintana-Ortí
author: Alfredo Remón
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: We address the numerical solution of Lyapunov, algebraic and differential Riccati equations, via the matrix sign function, on platforms equipped with general-purpose multicore processors and, optionally, one or more graphics processing units (GPUs). In particular, we review the solvers for these equations, as well as the underlying methods, analyze their concurrency and scalability and provide details on their parallel implementation. Our experimental results show that this class of hardware provides sufficient computational power to tackle large-scale problems, which only a few years ago would have required a cluster of computers.
Mathematics Subject Classification ID: 65F45
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65Y10
zbMATH DE Number: 7042191
zbMATH Keywords: control theory
zbMATH Keywords: Lyapunov and Riccati equations
zbMATH Keywords: high performance
zbMATH Keywords: multicore processors
zbMATH Keywords: GPUs
describes a project that uses: FLAME
MaRDI profile type: Publication
Wikidata QID: Q115224033
full work available at URL: https://doi.org/10.3390/a6040857
OpenAlex ID: W2043229868
cites work: Matrix Riccati equations in control and systems theory
cites work: Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
cites work: Parallel algorithms for model reduction of discrete-time systems
cites work: Solving linear-quadratic optimal control problems on parallel computers
cites work: A mixed-precision algorithm for the solution of Lyapunov equations on hybrid CPU-GPU platforms
cites work: Q5689624
cites work: Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search
cites work: Rosenbrock Methods for Solving Riccati Differential Equations
cites work: FLAME
cites work: A note on parallel matrix inversion
DOI: 10.3390/A6040857
Recommended article: Q4729238
Recommended article: Q3802494
Recommended article: Processor Efficient Parallel Solution of Linear Systems of Equations
Recommended article: Q3601070
description: scientific article; zbMATH DE number 7042191