On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction

On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction

We discuss the feasible interval of the parameter k and a general expression of matrix X which satisfies the rank equation r(A-BXC)=k. With these results, we study two problems under the rank constraint r(A-BXC)=k. The first one is to determine the maximal and minimal ranks under the rank constraint...

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Main Authors: Hongxing Wang, Yeguo Sun
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/457298
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spelling doaj-6d864263cb1244368fe2fc080f71394e2020-11-24T22:45:48ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/457298457298On Extremal Ranks and Least Squares Solutions Subject to a Rank RestrictionHongxing Wang0Yeguo Sun1Department of Mathematics and Computational Science, Huainan Normal University, Anhui 232038, ChinaDepartment of Mathematics and Computational Science, Huainan Normal University, Anhui 232038, ChinaWe discuss the feasible interval of the parameter k and a general expression of matrix X which satisfies the rank equation r(A-BXC)=k. With these results, we study two problems under the rank constraint r(A-BXC)=k. The first one is to determine the maximal and minimal ranks under the rank constraint r(A-BXC)=k. The second one is to derive the least squares solutions of ∥BXC-A∥F=min⁡ under the rank constraint r(A-BXC)=k.http://dx.doi.org/10.1155/2014/457298
collection DOAJ
language English
format Article
sources DOAJ
author Hongxing Wang
Yeguo Sun
spellingShingle Hongxing Wang
Yeguo Sun
On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction
Abstract and Applied Analysis
author_facet Hongxing Wang
Yeguo Sun
author_sort Hongxing Wang
title On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction
title_short On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction
title_full On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction
title_fullStr On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction
title_full_unstemmed On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction
title_sort on extremal ranks and least squares solutions subject to a rank restriction
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We discuss the feasible interval of the parameter k and a general expression of matrix X which satisfies the rank equation r(A-BXC)=k. With these results, we study two problems under the rank constraint r(A-BXC)=k. The first one is to determine the maximal and minimal ranks under the rank constraint r(A-BXC)=k. The second one is to derive the least squares solutions of ∥BXC-A∥F=min⁡ under the rank constraint r(A-BXC)=k.
url http://dx.doi.org/10.1155/2014/457298
work_keys_str_mv AT hongxingwang onextremalranksandleastsquaressolutionssubjecttoarankrestriction
AT yeguosun onextremalranksandleastsquaressolutionssubjecttoarankrestriction
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