报告题目: Solving the polynomial eigenvalue problem expressed in non-monomial basis by the scaled CORK linearization

报告人：谌鸿佳 副教授（南昌大学）

报告时间：2023年6月21日（周三）8:30-10:00

报告地点：海山楼A1101

校内联系人：杜磊 副教授

报告摘要：One of the most successful methods for solving a polynomial (PEP) or rational eigenvalue problem (REP) is to recast it, by linearization, as an equivalent but larger generalized eigenvalue problem which can be solved by standard eigensolvers. In this work, we investigate the backward errors of the computed eigenpairs incurred by the application of the well-received compact rational Krylov (CORK) linearization. Our treatment is unified for the PEPs or REPs expressed in various commonly used bases, including Taylor, Newton, Lagrange, orthogonal, and rational basis functions. We construct one-sided factorizations that relate the eigenpairs of the CORK linearization and those of the PEPs or REPs. With these factorizations, we establish upper bounds for the backward error of an approximate eigenpair of the PEPs or REPs relative to the backward error of the corresponding eigenpair of the CORK linearization. These bounds suggest a scaling strategy to improve the accuracy of the computed eigenpairs. We show, by numerical experiments, that the actual backward errors can be successfully reduced by scaling and the errors, before and after scaling, are both well predicted by the bounds

报告人简介：谌鸿佳，南昌大学数学与计算机学院副教授，2018年于日本筑波大学获得博士学位，2022年2月-2023年2月在香港浸会大学访问李仁仓教授。其主要研究方向为非线性特征值问题、矩阵方程以及数据科学中的聚类算法。主持国家自然科学基金青年基金和江西省自然科学基金各1项，相关成果发表于Journal of Scientific Computing, Numerical Linear Algebra with Applications等期刊。