Rank constrained matrix best approximation problem with respect to (skew) Hermitian matrices

In this literature, we study a rank constrained matrix approximation problem in the Frobenius norm: minr(X)=k‖BXB∗−A‖F2, where k is a nonnegative integer, A and X are (skew) Hermitian matrices. By using the singular value decomposition and the spectrum decomposition, we derive some conditions for th...

Full description

Saved in:
Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 319; pp. 77 - 86
Main Authors Liu, Xifu, Li, Wen, Wang, Hongxing
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2017
Subjects
Frobenius norm
Matrix approximation
Rank constrained matrix
Matrix approximation
Rank constrained matrix
15A24
Frobenius norm
Online AccessGet full text
ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2016.12.029

Cover

More Information
Summary:In this literature, we study a rank constrained matrix approximation problem in the Frobenius norm: minr(X)=k‖BXB∗−A‖F2, where k is a nonnegative integer, A and X are (skew) Hermitian matrices. By using the singular value decomposition and the spectrum decomposition, we derive some conditions for the existence of (skew) Hermitian solutions, and establish general forms for the (skew) Hermitian solutions to this matrix approximation problem.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.12.029