Two complementary block Macaulay matrix algorithms to solve multiparameter eigenvalue problems
type: Item
instance of: scholarly article
title: Two complementary block Macaulay matrix algorithms to solve multiparameter eigenvalue problems
zbMATH Open document ID: 1506.15010
author: Christof Vermeersch
author: B. De Moor
published in: Linear Algebra and its Applications
publication date: 2022-10-07T00:00:00Z
review text: The paper deals with Multiparameter Eigenvalue Problems (MEPs) which here are solved by two algorithms using the block Macaulay matrix. The first algorithm exploits the structure of the null space of the block Macaulay matrix in order to find the solution of the considered MEP, according to an approach already presented by the authors. On the other hand, the second algorithm considers the column space of the block Macaulay matrix. The intrinsic complementarity between both fundamental subspaces allows one to build a new complementary algorithm to solve MEPs. This column space based algorithm does not require an explicit computation of a numerical basis matrix of the null space, but considers the data in the columns of the block Macaulay matrix directly and removes the influence of the solutions at infinity implicitly via a backward QR-decomposition. Several significant numerical examples are reported to clarify the use of both algorithms.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 7597861
zbMATH Keywords: multiparameter eigenvalue problems
zbMATH Keywords: matrix pencils
zbMATH Keywords: block Macaulay matrix
zbMATH Keywords: realization theory
reviewed by: Raffaella Pavani
describes a project that uses: MultiParEig
MaRDI profile type: Publication
full work available at URL: j.laa.2022.08.014
OpenAlex ID: W4294862396
Wikidata QID: Q114151225
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DOI: 10.1016/J.LAA.2022.08.014
description: scientific article; zbMATH DE number 7597861