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EIGENVALUE DECOMPOSITION APPARATUS AND EIGENVALUE DECOMPOSITION METHOD

机译:特征值分解装置和特征值分解方法

摘要

The present invention provides an eigenvalue decomposition apparatus that can perform processing in parallel at high speed and high accuracy. The eigenvalue decomposition apparatus comprises a matrix dividing portion 14 that repeatedly divides a symmetric tridiagonal matrix T into two symmetric tridiagonal matrices, an eigenvalue decomposition portion 15 that performs eigenvalue decomposition on the symmetric tridiagonal matrix after the division, an eigenvalue computing portion 17 that repeatedly computes eigenvalues of the symmetric tridiagonal matrix that is the division origin and matrix elements of the symmetric tridiagonal matrix that is the division origin, based on eigenvalues and matrix elements obtained by eigenvalue decomposition performed by the eigenvalue decomposition portion 15, the matrix elements being part of elements of orthogonal matrices constituted by eigenvectors, until an eigenvalue of the symmetric tridiagonal matrix T is computed, and an eigenvector computing portion 19 that computes an eigenvector of the symmetric tridiagonal matrix T based on the symmetric tridiagonal matrix T and the eigenvalue thereof using twisted factorization.
机译:本发明提供了能够以高速和高精度并行执行处理的特征值分解装置。特征值分解装置包括将对称三对角矩阵T重复地分成两个对称三对角矩阵的矩阵划分部分 14 ,对对称矩阵进行特征值分解的特征值分解部分 15 分割后的三对角矩阵,一个特征值计算部分 17 ,该特征值计算部分重复计算作为分割原点的对称三对角矩阵的特征值,并基于特征值和由特征值分解部分 15 执行的特征值分解获得的矩阵元素,该矩阵元素是由特征向量构成的正交矩阵的元素的一部分,直到计算对称三对角矩阵T的特征值,并获得特征向量计算部分 19 ,该部分基于对称三角函数计算对称三对角矩阵T的特征向量Gonal矩阵T及其使用扭曲分解的特征值。

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