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Evaluation of small elements of the eigenvectors of certain symmetric tridiagonal matrices with high relative accuracy

机译:相对精确地评估某些对称三对角矩阵特征向量的小元素

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摘要

Evaluation of the eigenvectors of symmetric tridiagonal matrices is one of the most basic tasks in numerical linear algebra. It is a widely known fact that, in the case of well separated eigenvalues, the eigenvectors can be evaluated with high relative accuracy. Nevertheless, in general, each coordinate of the eigenvector is evaluated with only high absolute accuracy. In particular, those coordinates whose magnitude is below the machine precision are not expected to be evaluated with any accuracy whatsoever.
机译:对称三对角矩阵的特征向量的求值是数值线性代数中最基本的任务之一。众所周知的事实是,在特征值分离良好的情况下,可以以较高的相对精度评估特征向量。然而,通常,特征向量的每个坐标仅以很高的绝对精度进行评估。特别是,其大小低于机器精度的那些坐标预计不会以任何精度进行评估。

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