DIVIDE AND CONQUER THE CS DECOMPOSITION

作者：Sutton Brian D^*

来源：SIAM Journal on Matrix Analysis and Applications, 2013, 34(2): 417-444.

DOI：10.1137/120870785

• CS decomposition
• generalized singular value decomposition
• divide-and-conquer
• bidiagonal

We develop a divide-and-conquer algorithm for the bidiagonal CS decomposition (CSD). This complements an earlier algorithm based on simultaneous QR iteration. The new algorithm is designed to provide the efficiency gains of familiar divide-and-conquer algorithms on both serial and parallel architectures. The solution uses many components of existing algorithms, particularly the bidiagonal SVD algorithm of Gu and Eisenstat, but extra steps and reparameterizations are required to maintain orthogonality and consistent singular vectors, especially when the singular vectors are ill conditioned. The algorithm supports the stable computation of the generalized singular value decomposition (GSVD) in addition to the CSD.

• 出版日期2013