Differential equations for the analytic singular value decomposition of a matrix
Differential equations for the analytic singular value decomposition of a matrix
复制标题
DOI：
10.1007/bf01385862
复制
发表时间：
1992-12
影响因子：
2.1
通讯作者：
K. Wright
中科院分区：
文献类型：
--
作者：
K. Wright
本文研究了光滑依赖于参数的矩阵的光滑奇异值分解。以前的方法来解决这个问题是基于最小化技术，在这里，相比之下，一个系统的常微分方程推导出的分解。结果表明，与这些微分方程的初值问题的数值解提供了一个可行的方法来解决这个问题。特别考虑的情况下，出现的情况下，导致不确定性的数值解所需的评估与等模奇异值。举例说明该方法的行为。
This paper is concerned with finding a smooth singular value decomposition for a matrix which is smoothly dependent on a parameter. A previous approach to this problem was based on minimisation techniques, here, in contrast, a system of ordinary differential equations is derived for the decomposition. It is shown that the numerical solution of an initial value problem associated with these differential equations provides a feasible approach to the solution of this problem. Particular consideration is given to the situation which arises with equal modulus singular values which lead to indeterminacies in the evaluations needed for the numerical solution. Examples which illustrate the behaviour of the method are included.