Divide and conquer algorithm for computer simulation and application in the matrix eigenvalue problem
Divide and conquer algorithm for computer simulation and application in the matrix eigenvalue problem
复制标题
分而治之算法在矩阵特征值问题中的计算机模拟及应用
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Aimin Yang
中科院分区：
文献类型：
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作者：
Yuhuan Cui;Jingguo Qu;Weili Chen;Aimin Yang
DC是一种分而治之的方法。其基本思想是先将给定的真实的对称三对角矩阵A分解为两个低阶子矩阵A1、A2，然后将两个子矩阵的特征值粘在一起，通过计算求出原对称三角矩阵的特征值和特征向量。它是先求解子矩阵的特征值问题，然后再提出一个比原特征值问题更容易回答的问题。最后用计算机进行模拟，用数学软件编程分别求解各个子矩阵的特征值。
DC is a divide and conquers method for short. Its basic idea is to divide the given real symmetric tridiagonal matrix A into two lower-order submatrix A1 , A2 first, then glue the eigenvalues of the two submatrixes together and find the eigenvalue and eigenvector of the original symmetric triangular matrix by means of some calculations. It is that we solve the submatrix eigenvalue problem, and then pose a question easy to answer than the original eigenvalue problem. Finally we uses computer to simulate, using mathematical software programming to solve the elgenvalues of each submatrix separately.