矩阵分解在求解线性矩阵方程中的应用
首发时间:2010-12-09
摘要:矩阵的分解在最优化问题、特征值问题、最小二乘方问题、广义逆矩阵问题及统计学等方面都有着重要应用。本文中讨论和 分析了矩阵分解在求解线性矩阵方程组的最优解方面的应用。具体来说,本文中利用了矩阵的奇异值分解(SVD)及矩阵对的标准相关分解(CCD),在提出的三个问题的基础上,得出了问题Ⅰ、Ⅱ、Ⅲ的解的表示,并总结了类似问题的算法和算例。
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Matrix Decomposition in Solving Linear Matrix Equation Application
Abstract:Decomposition of matrics has important application in optimization, eigenvalue problems, least square method, generalized inverse matrix problems and statistics. In this paper, dicsuss and analyse the application of matrix decomposition to the optimal solution of linear matrix equation set. Specifically, by using SVD and CCD of matrix, solve the question I, II and III, summarize the similar algorithm and example.
Keywords: Liner Matrix Equation SVD(singular value decomposition) Nonsingular Matrix
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No.4394208543194129****
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