走向现代数学学术报告 - 汪祥教授（No. 668）

报告题目：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：2023年11月24日，15:00

腾讯会议：东海岸校区-D209

报告摘要：In this talk, we consider the quadratic eigenvalue problem (QEP) expressed in various commonly used bases, including Taylor, Newton, and Lagrange basis functions. We propose to investigate the backward errors of the computed eigenpairs and condition numbers of eigenvalues incurred by the application of the recently developed and well received compact rational Krylov (CORK) linearization. To improve the backward error and condition number of the QEP expressed in a non-monomial basis, we combine the tropical scaling with the CORK 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 CORK 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 CORK linearization. Our investigation is accompanied by adequate numerical experiments to justify our theoretical findings.

报告人简介：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和博士后流动站负责人，国家一流本科专业建设点负责人。担任中国工业与应用数学学会理事，中国数学会计算数学分会理事，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批成果。主持(含完成)国家自然科学基金面上、地区、青年项目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JSC、CCP、NLAA等权威期刊上共发表SCI收录论文50多篇。以第一完成人身份获江西省自然科学奖三等奖1项和江西省教学成果奖二等奖3项。