THE QR TRANSFORMATION .2.
THE QR TRANSFORMATION .2.
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DOI：
10.1093/comjnl/4.4.332
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发表时间：
1962-01-01
期刊：
影响因子：
1.4
通讯作者：
FRANCIS, JGF
中科院分区：
文献类型：
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作者：
FRANCIS, JGF
QR变换类似于基于么正变换的LR变换(Rutishauser，1958)。这两种变换都是求矩阵特征值的全局迭代方法，矩阵一般收敛到三角形。在本文的T1段中，我们简要地描述了QR变换，然后我们主要致力于证明收敛，主要结果如定理3所示。我们还表明，如果首先将矩阵约化为几乎三角形，将获得重要的优点(进一步的优点将变得明显)，并且我们概要地给出了一种改进收敛的方法。在本文的这一部分，我们考虑QR变换的实际应用。已经为Pegasus计算机编写了算法的两个版本；描述了这两个版本，并尝试对该方法进行评估。附录中给出了一些结果和详细的算法。第一部分发表于本卷的第265-71页(10月61号)。
The QR transformation is an analogue to the LR transformation (Rutishauser, 1958) based on unitary transformations. Both these transformations are global iterative methods for finding the eigenvalues of a matrix, the matrix converging in general to triangular form. In Par t1 of this paper the QR transformation was briefly described and we were then principally concerned with proving convergence, the main result being expressed in theorem 3. We also showed that if the matrix is first reduced to almost triangular form important advantages are gained (further advantages will become apparent) and we gave in outline a way in which convergence could be improved. In this part of the paper we consider the practical application of the QR transformation. Two versions of the algorithm have been programmed for the Pegasus computer; these are described and an attempt is made to evaluate the method. Some results and detailed algorithms are given in appendices. Part 1 was published on pp. 265–71 of this volume (Oct. 61).