Low-Rank Positive Approximants of Symmetric Matrices
Low-Rank Positive Approximants of Symmetric Matrices作者机构：Hydrological Service Jerusalem Israel
出 版 物：《Advances in Linear Algebra & Matrix Theory》 (线性代数与矩阵理论研究进展（英文）)
年 卷 期：2014年第4卷第3期
页 面：172-185页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Low-Rank Positive Approximants Unitarily Invariant Matrix Norms
摘 要：Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which is nearest to X in a certain matrix norm. The problem is first solved with regard to four common norms: The Frobenius norm, the Schatten p-norm, the trace norm, and the spectral norm. Then the solution is extended to any unitarily invariant matrix norm. The proof is based on a subtle combination of Ky Fan dominance theorem, a modified pinching principle, and Mirsky minimum-norm theorem.
维普期刊数据库