报告题目：Conquering algebraic nonlinearity in nonlinear eigenvalue problems
报告人：邵美悦 研究员（复旦大学）
报告时间：2022年12月15日（星期四）10:00-11:00
报告地点：腾讯会议：706-817-154 密码:1111
校内联系人：董波 教授 联系电话：84708351-8026
报告摘要：In several real world applications of nonlinear eigenvalue problems, functions with branch points appear in the nonlinear matrix-valued functions. This type of nonlinear eigenvalue problems is challenging to tackle because existing nonlinear eigenvalue algorithms usually require the matrix-valued function to be analytic in the region where the desired eigenvalues are located. We propose two approaches to handle the algebraic nonlinearity. The first approach is to solve the nonlinear eigenvalue problem through linearization. Unlike existing approximation-based approaches which typically aim at finding only a few eigenvalues, the linearization technique can be used to reliably compute all eigenvalues counting algebraic multiplicity. The second approach, mainly for computing a few eigenvalues in a certain region, is to apply appropriate transformations of variables after a possible subdivision of the region of interest. The transformed nonlinear matrix-valued functions are always analytic inside its corresponding subregion, and can be approximated by low order rational approximations due to their analyticity. We are then free to use a nonlinear eigenvalue solver of choice to solve the remaining problem.
报告人简介：邵美悦，复旦大学大数据学院青年研究员，主要研究领域为数值线性代数、高性能计算、量子力学计算。2014年毕业于瑞士洛桑联邦理工学院，获得计算数学博士学位。2014年至2019年在美国劳伦斯伯克利国家实验室从事研究工作，先后担任博士后研究员和项目科学家。2019年5月进入复旦大学大数据学院工作。
