We study the issue of numerically solving inverse singular value problems (ISVPs). Motivated by the Newton-type method introduced in [3] for solving ISVPs with distinct and positive singular values, we propose an extended Newton-type method working for ISVPs with multiple and/or zero singular values. Because of the absence of some important and crucial properties, the approach/technique used in the case of distinct and positive singular values no longer works for the case of multiple and/or zero singular values, and we develop a new approach/technique to treat the case of multiple and/or zero singular values. Under the standard nonsingularity assumption of the relative generalized Jacobian matrix at a solution, the quadratic convergence result is established for the extended Newton-type method, and numerical experiments are provided to illustrate the convergence performance of the extended method. Our extended method and convergence result in the present paper improve and extend...

中文翻译：

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具有多个和/或零个奇异值的反奇异值问题的扩展牛顿型方法

我们研究数值解反奇异值问题（ISVP）的问题。受[3]中引入的牛顿型方法求解具有独特和正奇异值的ISVP的启发，我们提出了一种扩展牛顿型方法，适用于具有多个和/或零奇异值的ISVP。由于缺少一些重要的重要特性，因此在出现明显和正的奇异值时使用的方法/技术不再适用于多个和/或零奇异值的情况，因此我们开发了一种新的方法/技术来处理多个和/或零个奇异值的情况。在解决方案中相对广义雅可比矩阵的标准非奇点假设下，针对扩展牛顿型方法建立了二次收敛结果，并通过数值实验说明了扩展方法的收敛性能。我们的扩展方法和收敛结果在本文中得到了改进和扩展。