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

被引：4

作者：

Wang, Hongxing ^{[1
]}

机构：

[1] Guangxi Univ Nationalities, Sch Sci, Guangxi Key Lab Hybrid Computat & IC Design Anal, Nanning 530006, Peoples R China

来源：

CALCOLO | 2019年 / 56卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Matrix approximation problem; Rank-constrained matrix; SVD; Q-SVD; DIMENSIONALITY REDUCTION; RECONSTRUCTION; SOLVABILITY; IMPROVEMENT; ACCURACY;

D O I：

10.1007/s10092-019-0339-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the following rank-constrained matrix approximation problem in the Frobenius norm: parallel to C-AX parallel to = min subject to rk(C-1 - A(1)X) = 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.

引用

页数：18

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