Constrained Low Rank Approximation of the Hermitian Nonnegative-Definite Matrix

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 Ω is the set of the Hermitian nonnegative-definite least squares solution to the matrix equation AXA B * = . 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.