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学术报告-魏益民

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2021-03-26 08:34:00

学术报告


题      目: Time-varying Generalized Tensor Eigen-analysis via Dynamic Methods


报  告  人:魏益民   教授  (邀请人:彭小飞 )

                                   复旦大学



时      间:2021-03-26  10:00--11:00


地      点:学院401


报告人简介:

        魏益民,复旦大学教授、博士生导师,获上海市自然科学三等奖,为上海市高校优秀青年教师和上海市“曙光”学者称号获得者。主要从事矩阵/张量方面的理论和应用研究,在《SIAM J.Matrix Anal. Appl.》《SIAM J. Numer. Anal.》《SIAM J. Sci. Comput.》《J. Sci. Comput.》等权威学术期刊发表论文一百余篇,出版中英文专著3部,英文版教材1部。多次主持国家自然科学基金面上项目、教育部博士点基金项目和973子课题等项目,为《Comput. Appl.Math.》、《J. Appl. Math. Comput.》和《高校计算数学学报》编委。


摘      要:

       Eigen-analysis of matrices with parameters has a long history. When the parameter is time, or the matrix is time-dependent, the Zhang neural networks for the time-varying matrix problem have been developed in recent years. Motivated by tensor generalized eigenvalues and the Zhang dynamics method, we investigate the time-varying eigenpair of symmetric tensors. A continuous Zhang dynamics model is given to compute the tensor eigenpairs, such as the H- and Z-eigenpairs. In order to accelerate the convergence, a modified Zhang dynamics model is also presented. Moreover, the generalized tensor/matrix eigenpairs could also be computed by the two proposed models. Theoretical analysis of the convergence and robustness are provided. We also test some numerical examples which illustrate that the two proposed models are effective.