报告人：董波 教授
报告题目：Numerical method for singular multiparameter eigenvalue problems
报告时间：2026年5月8日（周五）上午10：00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
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、矩阵特征值问题等，在SINUM、SIMAX、Math. Comput.、Numer. Math.、J. Sci. Comput. 等期刊上发表论文多篇，主持国家自然科学基金4项。
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.