Abstract

The computation of the eigenvalue decomposition of matrices is one of the most investigated problems in numerical linear algebra. In particular, real nonsymmetric tridiagonal eigenvalue problems arise in a variety of applications. In this paper the problem of computing an eigenvector corresponding to a known eigenvalue of a real nonsymmetric tridiagonal matrix is considered, developing an algorithm that combines part of a \(QR\) sweep and part of a \(QL\) sweep, both with the shift equal to the known eigenvalue. The numerical tests show the reliability of the proposed method.

中文翻译：

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计算非对称三对角矩阵的特征向量

摘要

矩阵特征值分解的计算是数值线性代数中研究最多的问题之一。特别是，实数非对称三对角特征值问题出现在各种应用中。在本文中，考虑了计算与实数非对称三对角矩阵的已知特征值相对应的特征向量的问题，开发了一种将\(QR\)扫描的一部分和\(QL\)扫描的一部分相结合的算法，两者都具有位移等于已知特征值。数值试验表明了所提出方法的可靠性。