报告题目：Extended Newton-type method for inverse singular value problems with multiple and/or zero singular values
报 告 人：李冲 (浙江大学 教授)
报告时间：2023年11月10日 10:45开始
报告地点：9-218
报告摘要：In this talk, we study the issue of numerically solving inverse singular value problems (ISVPs). Motivated by the Newton-type method introduced 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 significantly the corresponding ones for the special cases with distinct positive singular values and/or for the square case.
报告人简介：李冲，浙江大学数学系教授，博士生导师。主要从事非线性优化理论与计算、数值泛函分析、数值代数、稀疏优化及其应用、机器学习等领域的研究。先后主持国家自然科学基金及省部级项目等近二十项，出版专著1部，在SCI期刊上发表论文近200篇， 特别是在优化理论和计算数学的顶级刊物SIAM J Optim., Math. Program，SIAM J. Control Optim.以及SIAM J.Numer. Anal上发表论文近30篇。1992年起享受国务院政府特殊津贴，原商业部有突出贡献的中青年专家、江苏省第七届青年科学家等，2004年获教育部首届新世纪优秀人才计划资助。
