報告人：董波 教授
報告題目：Numerical method for singular multiparameter eigenvalue problems
報告時間：2026年5月8日（周五）上午10：00
報告地點：云龍校區6號樓304報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
董波，大連理工大學數學科學學院教授、博士生導師。主要的研究工作包括非線性方程組全部解問題、矩陣特征值問題等，在SINUM、SIMAX、Math. Comput.、Numer. Math.、J. Sci. Comput. 等期刊上發表論文多篇，主持國家自然科學基金4項。
報告摘要：
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.