报告题目：A locally and cubically convergent algorithm for computing Z-eigenpairs of symmetric tensors

报 告 人：郑兵教授（兰州大学）

报告时间：2024年4月29日  10:00-11:00

报告地点：格物楼数学研究中心528

报告摘要：

In this talk, we are concerned with computing Z-eigenpairs of symmetric tensors. We first show that computing Z-eigenpairs of a symmetric tensor is equivalent to solving the nonzero solutions of a nonlinear system of equations, and then propose a modified normalized Newton method (MNNM) for it. Our proposed MNNM method is proved to be locally and cubically convergent under some suitable conditions, which greatly improves the Newton correction (NCM) method and the O-NCM method provided by Jaffe, Weiss and Nadler (SIAM J. Matrix Anal. Appl., 39: 1071-1094, 2018)(the NCM and O-NCM methods only enjoy a quadratic rate of convergence). As an application, the unitary symmetric eigenpairs (US-eigenpairs) of a complex-valued symmetric tensor arising from the computation of quantum entanglement in quantum physics are calculated by the MNNM method. Some numerical experiments are performed to illustrate the efficiency and effectiveness of our proposed method.

报告人简介：

郑兵，兰州大学数学与统计学院教授、博士生号师。长期从事数值代数、神经网络算法的研究工作，负责承担国家自然科学基金面上项目、教育部外国专家重点项目、甘肃省自然科学基金项目等10余项。多次应邀赴美国、日本、西班牙、俄罗斯、印度以及香港、澳门等国家和地区参加学术会议并做学术报告，并先后在印度统计研究所新德里中心和美国Emory大学数学与计算机科学系做访问学者。迄今已在《SIAM J. Matrix Anal. Appl.》《J. Math. Anal. Appl.》《J. Optim. Theory Appl.》《Inverse Problems》《Linear Algebra Appl.》《J. Multivariate Anal.》《Adv. Comput. Math.》《Numer. Linear Algebra Appl.》《IEEE Trans. Neural Netw. Learn. Syst.》以及《Automatica》等国内外重要刊物上发表论文百余篇。2005年荣获甘肃省第十二届高校青年教师成才奖。