报告人： 魏益民 教授 （复旦大学）

时间： 6月2日（周五）下午3:00--4:00

地点： 理科楼A404

报告摘要：In this talk, we propose the tensor Noda iteration (NI) and its inexact version for solving the eigenvalue problem of a particular class of tensor pairs called generalized M[1]tensor pairs. A generalized M-tensor pair consists of a weakly irreducible nonnegative tensor and a nonsingular M-tensor within a linear combination. It is shown that any generalized M-tensor pair admits a unique positive generalized eigenvalue with a positive eigenvector. A modified tensor Noda iteration (MTNI) is developed for extending the Noda iteration for nonnegative matrix eigenproblems. In addition, the inexact generalized tensor Noda iteration method (IGTNI) and the generalized Newton-Noda iteration method (GNNI) are also introduced for more efficient implementations and faster convergence. Under a mild assumption on the initial values, the convergence of these algorithms is guaranteed. The efficiency of these algorithms is illustrated by numerical experiments.

报告人简介：魏益民，复旦大学教授、博士生导师。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。主持国家自然科学基金面上项目、教育部博士点基金项目等，为《Comput. Appl.Math.》、《J. Appl. Math. Comput.》和《高校计算数学学报》编委。