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对称矩阵填充的线性交替最速下降算法研究

Journal of North University of China(Natural Science Edition)(2018)

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Abstract
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.
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Key words
matrix completion,symmetric matrix,alternating minimization,gradient descent,inexact linear search
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