求解对称半正定矩阵低秩逼近的乘性迭代算法

Multiplicative iterative algorithm for the low rank approximation of the symmetric positive semi-definite matrix

为求解对称半正定矩阵低秩逼近问题,基于矩阵的满秩分解和非负矩阵分解算法,构造了一种新的乘性迭代算法,并给出了新算法的收敛性定理。数值实验表明,与Cadzow算法相比,新算法更可行高效。

In order to solve the low rank approximation of the symmetric positive semi-definite matrix,a new multiplicative iterative algorithm is constructed based on the full rank factorization of the matrix and the algorithm for the non-negative matrix factorization,the convergence theorem for the proposed algorithm is given.Numerical experiments show that com-pared with the Cadzow algorithm,the new algorithm is feasible and efficient.