无Cayley变换的两步算法用于逆奇异值问题
A Cayley-free Two-Step Algorithm for Inverse Singular Value Problems
AI总结：
本文提出了一种无Cayley变换的两步算法，用于高效求解逆奇异值问题，具有立方根收敛速度。
摘要：
本文研究了出现在各种应用中的逆奇异值问题（简称ISVP）的数值解法。受逆特征值问题方法的启发，我们提出了一种无Cayley变换的两步算法来求解ISVP。与现有的ISVP两步算法相比，我们的算法消除了对Cayley变换的需求，从而在每次外迭代计算近似奇异向量时避免了求解2(m+n)个线性系统。在假设解处的雅可比矩阵非奇异的情况下，我们对所提算法进行了收敛性分析，并证明了其立方根收敛速度。进行了数值实验以验证我们算法的有效性。
英文摘要：
In this paper, we investigate numerical solutions for inverse singular value problems (for short, ISVPs) arising in various applications. Inspired by the methodologies employed for inverse eigenvalue problems, we propose a Cayley-free two-step algorithm for solving the ISVP. Compared to the existing two-step algorithms for the ISVP, our algorithm eliminates the need for Cayley transformations and consequently avoids solving $2(m+n)$ linear systems during the computation of approximate singular vectors at each outer iteration. Under the assumption that the Jacobian matrix at a solution is nonsingular, we present a convergence analysis for the proposed algorithm and prove a cubic root-convergence rate. Numerical experiments are conducted to validate the effectiveness of our algorithm.
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