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.
<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.
作者
Haixia Chang
Haixia Chang(School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, China)
