High order approximations of the operator Lyapunov equation have low rank
type: Item
instance of: scholarly article
title: High order approximations of the operator Lyapunov equation have low rank
zbMATH Open document ID: 1503.65296
author: Luka Grubišić
author: Harri Hakula
published in: BIT
publication date: 2022-11-22T00:00:00Z
review text: When dealing with non-local operators, low-rank approximation methods are turning out to be a method of choice both for theoretical analysis as well as a foundation for constructing high performance numerical algorithms. This work presents a low-rank greedily adapted \(hp\)-finite element algorithm for computing an approximation to the solution of the Lyapunov operator equation. The authors show that there is a hidden regularity in eigenfunctions of the solution of the Lyapunov equation which can be utilized to justify the use of high-order finite element spaces. Numerical experiments indicate that they achieve eight figures of accuracy for computing the trace of the solution of the Lyapunov equation posed in a dumbbell-domain using a finite element space of dimension of only 104 degrees of freedom. Even more surprising is the observation that the \(hp\)-refinement has an effect of reducing the rank of the approximation of the solution.
reviewed by: Xiaodi Zhang
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 7621792
zbMATH Keywords: low-rank approximation
zbMATH Keywords: exponential decay
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: \(hp\)-finite element methods
MaRDI profile type: Publication
Wikidata QID: Q114227185
full work available at URL: s10543-022-00917-z
OpenAlex ID: W4226300631
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DOI: 10.1007/S10543-022-00917-Z
description: scientific article; zbMATH DE number 7621792