题目：利用缩放技术求解非单项式基底表示的二次特征值问题
Solving the quadratic eigenvalue problem expressed in non-monomial basis by the scaling techniques.
报告人：汪祥 教授（南昌大学）
报告时间：2025年6月27日 10：15-11：15
报告地点：文友楼314
摘要：
In this paper, we consider the quadratic eigenvalue problem (QEP) expressed in various commonly used bases, including Taylor, Newton, and Lagrange bases. We propose to investigate the backward errors of the computed eigenpairs and condition numbers of eigenvalues for QEP solved by a class of block Kronecker linearizations. To improve the backward error and condition number of the QEP expressed in a non-monomial basis, we combine the tropical scaling with the block Kronecker linearization. We then establish upper bounds for the backward error of an approximate eigenpair of the QEP relative to the backward error of an approximate eigenpair of the block Kronecker linearization with and without tropical scaling. Moreover, we get bounds for the normwise condition number of an eigenvalue of the QEP relative to that of the block Kronecker linearization. Our investigation is accompanied by adequate numerical experiments to justify our theoretical findings.
个人简介：
汪祥，博士、教授、博士生导师，现任南昌大学数学与计算机学院副院长，南昌大学数学一级学科博士学位点负责人。获批多个省级人才称号，担任CSIAM理事，中国计算数学分会理事，中国高等教育学会教育数学专委会副秘书长, 国家天元数学东南中心执委会委员，国际知名期刊《Computational and Applied Mathematics》的副主编。主要从事数值代数、人工智能与数据科学等领域的研究，在大规模稀疏线性方程组、大规模稀疏特征值问题、线性和非线性矩阵方程的数值求解、谱聚类等方面取得了一些成果。目前主持(含完成)国家自然科学基金4项及省部级项目十几项。近几年以第一作者或通讯作者在ACM、JSC、CCP、NLAA等权威期刊上共发表SCI收录论文80多篇。以第一完成人身份获江西省自然科学奖1项和江西省教学成果奖3项。
