一、题 目: Riemannian Newton-CG Methods for Constructing a Positive Doubly Stochastic Matrix from Spectral Data
二、主讲人：白正简教授（厦门大学）
三、时 间：2020年11月12日（周四）上午：9:30-10:30
四、地点：线上 腾讯ID:186 527 174
摘要：In this paper, we consider the inverse eigenvalue problem for the positive doubly stochastic matrices, which aims to construct a positive doubly stochastic matrix from the prescribed realizable spectral data. By using the real Schur decomposition, the inverse problem is written as a nonlinear matrix equation on a matrix product manifold. We propose monotone and nonmonotone Riemannian inexact Newton-CG methods for solving the nonlinear matrix equation. The global and quadratic convergence of the proposed methods is established under some assumptions. We also provide invariant subspaces of the constructed solution to the inverse problem based on the computed real Schur decomposition. Finally, we report some numerical tests, including an application in digraph, to illustrate the effectiveness of the proposed methods.
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报告人简介：白正简，厦门大学教授，博士生导师，教育部“新世纪优秀人才支持计划”入选者，曾获2009年度“福建省科学技术奖二等奖”和中国计算数学学会“应用数值代数奖”。主要研究方向包括数值线性代数、矩阵特征值反问题、非线性特征值问题以及矩阵流形上的优化算法等，已在包括SIAM J. Numer. Anal., SIAM J. Matrix Anal. Appl., SIAM J. Sci. Comput., Inverse Problems, Numerische Mathematik, Mech. Syst. Signal Process.等国际著名期刊上发表SCI学术论文三十余篇，曾多次应邀在学术会议上作邀请报告或分组报告。先后主持国家自然科学基金青年项目1项、面上项目2项和福建省杰出青年科学基金项目1项。现为中国计算数学学会第九届理事会理事。
