The Orthogonal qd-Algorithm
The Orthogonal qd-Algorithm
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正交 qd 算法
DOI：
10.1137/s1064827594274887
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
U. Matt
中科院分区：
文献类型：
--
作者：
U. Matt
提出了计算双对角矩阵奇异值分解的正交qd算法。该算法是Rutishauser的qd算法的一种改进，它能够以较高的相对精度确定所有的奇异值及其相应的奇异向量。一个推广的吉文斯变换，除了正交QD算法的应用程序，也介绍了。
正交QD算法的移位策略基于Laguerre方法，该方法用于计算双对角矩阵的最小奇异值的下界。特别注意的是，致力于数值稳定的这种转变的评价。
The orthogonal qd-algorithm is presented to compute the singular value decomposition of a bidiagonal matrix. This algorithm represents a modification of Rutishauser's qd-algorithm, and it is capable of determining all the singular values and their corresponding singular vectors to high relative accuracy. A generalization of the Givens transformation, which has applications besides the orthogonal qd-algorithm, is also introduced.
The shift strategy of the orthogonal qd-algorithm is based on Laguerre's method, which is used to compute a lower bound on the smallest singular value of the bidiagonal matrix. Special attention is devoted to the numerically stable evaluation of this shift.