报告题目：Numerical method for singular multiparameter eigenvalue problems

报 告 人：董波教授（大连理工大学）

报告时间：2025年1月16日  9:00-9:45

报告地点：格物楼528

报告摘要：

Multiparameter eigenvalue problems arising in applications, such as the model updating problems, bivariate polynomial systems, aeroelastic flutter problems are often sparse and singular. The theoretical analysis and numerical algorithms for this problem are fundamental different from those for the nonsingular problems. In this talk, I will give two classes of methods to solve a singular multiparameter eigenvalue problem, one is the numerical method by transforming it to a simultaneous eigenvalue problem,the other is the homotopy method. For the former, we apply the row-column compress method to reduce the size of the problem. For the latter, to overcome the difficulty of computational complexity, we use random product homotopy to cut down the number of invalid paths. Moreover, a more accurate upper bound of the number of solutions, i.e. the number of generated paths, is presented. Also one practical example and several random examples are presented to validate the effectiveness and efficiency of the method.

报告人简介：

董波，大连理工大学数学科学学院教授、博士生导师。主要的研究工作包括非线性方程组全部解问题、矩阵特征值问题、张量分析等，主持省部级以上基金4项，在SINUM、SIMAX、Math. Comput.、Numer. Math、J. Sci. Comput.等计算数学著名期刊上发表论文20余篇。