TITLE:
Constrained Low Rank Approximation of the Hermitian Nonnegative-Definite Matrix
AUTHORS:
Haixia Chang
KEYWORDS:
Low Rank Approximation, Hermitian Matrix, Nonnegative-Definite Matrix, Least Square
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.10 No.2,
June
29,
2020
ABSTRACT: In this paper, we consider a
constrained low rank approximation problem: , where E is a given complex matrix, p is a
positive integer, and is the set of
the Hermitian nonnegative-definite least squares solution to the matrix
equation . We discuss the range of p and derive the corresponding explicit solution expression of the
constrained low rank approximation problem by matrix decompositions. And an
algorithm for the problem is proposed and the numerical example is given to
show its feasibility.