Constrained Low Rank Approximation of the Hermitian Nonnegative-Definite Matrix

• 作者: Haixia Chang
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: Low Rank Approximation Hermitian Matrix Nonnegative-Definite Matrix Least Square
• 年，卷（期）: 2020,（2）
• 页码范围: 22-33
• 页数: 12页
• 分类号: O17

摘要

<span style="line-height:1.5;"><span>In this paper, we consider a constrained low rank approximation problem: </span><img src="Edit_57d85c54-7822-4512-aafc-f0b0295a8f75.png" width="100" height="24" alt="" /></span><span style="line-height:1.5;"><span>, where </span><i><span>E</span></i><span> is a given complex matrix, </span><i><span>p</span></i><span> is a positive integer, and </span></span><span style="line-height:1.5;"></span><span style="line-height:1.5;"><span> is the set of the Hermitian nonnegative-definite least squares solution to the matrix equation </span><img src="Edit_ced08299-d2dc-4dbb-907a-4d8d36d2e87a.png" width="60" height="16" alt="" /></span><span style="line-height:1.5;"><span>. We discuss the range of </span><i><span>p</span></i><span> 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.