A contribution to the theory and practice of the block Kogbetliantz method for computing the SVD
A contribution to the theory and practice of the block Kogbetliantz method for computing the SVD
复制标题
对计算 SVD 的分块 Kogbetliantz 方法的理论和实践的贡献
DOI：
10.1007/s10543-012-0388-y
复制
发表时间：
2012
影响因子：
1.5
通讯作者：
Z. Drmač
中科院分区：
文献类型：
--
作者：
Zvonimir Bujanovic;Z. Drmač
本文研究了用于计算一般实数或复数矩阵奇异值分解（SVD）的块版Kogbetliantz算法的收敛性和实际实现。证明了简单奇异值和奇异向量的全局收敛性，包括渐近二次化到对角形式。对于某些平行块支点策略也能保证收敛性。这弥补了理论差距，为块算法的并行实现提供了坚实的理论基础，并提供了有价值的见解。
This article studies the convergence and practical implementation of the block version of the Kogbetliantz algorithm for computing the singular value decomposition (SVD) of general real or complex matrices. Global convergence is proved for simple singular values and the singular vectors, including the asymptotically quadratic reduction to diagonal form. The convergence can be guaranteed for certain parallel block pivot strategies as well. This bridges a theoretical gap, provides solid theoretical basis for parallel implementations of the block algorithm, and provides valuable insights.