Minimum rank positive semidefinite solution to the matrix approximation problem in the spectral norm. (September 2020)

• Record Type: Journal Article
• Authors: Liu, Xifu; Luo, Le
• Is Part Of: Applied mathematics letters. Volume 107(2020)
• Publication Date: 2020-09
• Subjects: Matrix approximation -- Positive semidefinite solution -- Minimum rank -- Spectral norm; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106408
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we discuss the following minimum rank matrix approximation problem in the spectral norm: min X ⩾ 0 r ( X ) subject to ‖ A − B X B ∗ ‖ 2 = min, where A ∈ ℂ ⩾ m × m and B ∈ ℂ m × n . By using the positive-semidefinite-type generalized singular value decomposition, we derive the expressions of the minimum rank and the minimum rank positive semidefinite solution to the above matrix approximation problem.