On singular values of partially prescribed matrices
type: Item
instance of: scholarly article
title: On singular values of partially prescribed matrices
zbMATH Open document ID: 1155.15006
author: Pedro M. Q. Aguiar
author: Marko Stošić
author: João Xavier
published in: Linear Algebra and its Applications
publication date: 2008-10-06T00:00:00Z
review text: Motivated by problems coming from computer vision, this paper solves the problem of determining the possible values of the \(p\)th singular value of a partially prescribed matrix in the case when the set of unknown entries has the form of a Young diagram. A complete solution for the generic matrix is given. It is shown that an arbitrary matrix can be completed such that the resulting matrix has the \(p\)th singular value arbitrarily close to a theoretical minimum. A fast and efficient algorithm for the determination of the unknown entries is provided. A second problem of determining the possible \(p\)th singular value of a given matrix under a specified rank one perturbation is solved.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 5349177
zbMATH Keywords: singular value
zbMATH Keywords: matrix completion
zbMATH Keywords: rank deficiency matrix
zbMATH Keywords: inverse problem
zbMATH Keywords: Young diagram
zbMATH Keywords: algorithm
zbMATH Keywords: rank one perturbation
reviewed by: C. M.da Fonseca
MaRDI profile type: Publication
full work available at URL: j.laa.2008.06.021
OpenAlex ID: W2015886551
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DOI: 10.1016/J.LAA.2008.06.021
description: scientific article; zbMATH DE number 5349177