Computing the complete CS decomposition
Computing the complete CS decomposition
复制标题
计算完整的 CS 分解
DOI：
10.1007/s11075-008-9215-6
复制
发表时间：
2007
影响因子：
2.1
通讯作者：
Brian D. Sutton
中科院分区：
文献类型：
--
作者：
Brian D. Sutton
给出了一种计算分块酉矩阵完全CS分解的算法。虽然CS分解（CSD）的存在自1977年以来已被确认，以前的算法计算只有一个减少的版本。这个简化的版本，可以称为2 × 1 CSD，等价于两个同时的奇异值分解。本文提出的算法计算完整的2 × 2 CSD，这需要同时对角化划分为2 × 2块结构的酉矩阵的所有四个块。该算法似乎是唯一可用的完全指定的算法。计算分两个阶段进行。在第一阶段，酉矩阵被简化为双对角块形式，如萨顿和Edelman所描述的。在第二阶段中，使用Golub，Kahan，Reinsch和Demmel的双对角SVD算法的技术同时对角化块。该算法具有许多理想的数值特征。
An algorithm for computing the complete CS decomposition of a partitioned unitary matrix is developed. Although the existence of the CS decomposition (CSD) has been recognized since 1977, prior algorithms compute only a reduced version. This reduced version, which might be called a 2-by-1 CSD, is equivalent to two simultaneous singular value decompositions. The algorithm presented in this article computes the complete 2-by-2 CSD, which requires the simultaneous diagonalization of all four blocks of a unitary matrix partitioned into a 2-by-2 block structure. The algorithm appears to be the only fully specified algorithm available. The computation occurs in two phases. In the first phase, the unitary matrix is reduced to bidiagonal block form, as described by Sutton and Edelman. In the second phase, the blocks are simultaneously diagonalized using techniques from bidiagonal SVD algorithms of Golub, Kahan, Reinsch, and Demmel. The algorithm has a number of desirable numerical features.
DOI：
--
发表时间：
2007
期刊：
Lecture Notes in Computer Science(Springer-Verlag) 4671
影响因子：
--
作者：
Yamamoto;Y.;Fukaya;T.;Uneyama;T.;Takata;M.;Kimura;K.;Iwasaki;M;Nakamura;Y
通讯作者：
Y