Work

Generalized low-rank approximation to the symmetric positive semidefinite matrix

Year: 2025

Type: article

Abstract: In this paper, we consider the generalized low-rank approximation to the symmetric positive semidefinite matrix in the Frobenius norm: $ \underset{X}{\min} \sum^{m}_{i = 1}\left \Vert A_{i}-B_{i}XB_{i}^{T}\right \Vert^{2}_{F}, $ where $ X $ is an unknown symmetric positive semidefinite matrix whose rank is less than or equal to a positive integer $ k $. We first characterize the feasible set as $ X = YY^{T} $, where $ Y $ has the order $ n\times k $, and then convert the generalized low-rank approximation into an unconstrained generalized optimization problem. Finally, we employ the nonlinear conjugate gradient method with an exact line search to solve the generalized optimization problem. We also give numerical examples to exemplify the results.

Source: AIMS Mathematics

DOI: 10.3934/math.2025368

Authors: Haixia Chang, Chunmei Li, Longsheng Liu

Institutions: Shanghai Lixin University of Accounting and Finance, Guilin University of Electronic Technology, Anqing Normal University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Natural Science Foundation of China, Natural Science Foundation of Guangxi Province