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Calcolo
Published in: Calcolo 4/2019

01-12-2019

Least squares solutions to the rank-constrained matrix approximation problem in the Frobenius norm

Author: Hongxing Wang

Published in: Calcolo | Issue 4/2019

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Abstract

In this paper, we discuss the following rank-constrained matrix approximation problem in the Frobenius norm: \(\Vert C-AX\Vert =\min \) subject to \( \text{ rk }\left( {C_1 - A_1 X} \right) = b \), where b is an appropriate chosen nonnegative integer. We solve the problem by applying the classical rank-constrained matrix approximation, the singular value decomposition, the quotient singular value decomposition and generalized inverses, and get two general forms of the least squares solutions.
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Metadata
Title
Least squares solutions to the rank-constrained matrix approximation problem in the Frobenius norm
Author
Hongxing Wang
Publication date
01-12-2019
Publisher
Springer International Publishing
Published in
Calcolo / Issue 4/2019
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-019-0339-y

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