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.
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页数：18
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