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Constrained Low Rank Approximation of the Hermitian Nonnegative-Definite Matrix
School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, China
- 1 School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, China
Advances in Linear Algebra & Matrix Theory·Volume 10 (2020)·Pages 22–33·Published 30 April 2020·DOI10.4236/alamt.2020.102003
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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.
KeywordsLow Rank ApproximationHermitian MatrixNonnegative-Definite MatrixLeast Square
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