对称矩阵填充的线性交替最速下降算法研究

The Linear Alternating Steepest Descent Algorithm Research for Symmetric Matrix Completion

研究了对称矩阵填充的相关算法.利用对称矩阵可对角化的性质,将对称矩阵简单因式分解.通过对每一部分求导数,找到最速下降方向.沿着最速下降方向结合非精确线性搜索方法求得对应的最优步长,进一步更新迭代后的矩阵.最后通过分析误差,精确地填充对称矩阵.理论上证明了算法的收敛性.并通过取不同的采样密度进行数值实验进一步验证了算法的可行性和有效性.

The correlation algorithm of symmetric matrix completion was studied. Through using the property of symmetric matrices can be diagonalized, the symmetric matrix was simply factorized. By finding the derivative of each part, the steepest descent direction was obtained. Along the steepest descent direction, combined with the inexact linear search method to get the corresponding optimal step size, and further update the iterative matrix. Finally, by analyzing the error, the symmetric matrix was completed accurately. In theory, the convergence of the algorithm was proved. In experiment, the numerical experiment was carried out by taking different sampling density to verify the feasibility and validity of the algorithm.