题目：Riemannian Newton-CG Methods for Constructing a Positive
时间：2020年10月28日（周三）16:00-17:00
地点：立志楼A422
主办：数学与计算科学学院
报告人简介：
      白正简：厦门大学数学科学学院教授，博士生导师。现任中国计算数学学会第九届理事会理事。教育部新世纪优秀人才支持计划获得者，福建省杰出青年科学基金获得者。从事数值线性代数、非线性特征值问题、特征值反问题及其数值最优化方法、黎曼流形上的优化算法等方面研究。近期发表SCI论文40余篇，其中在SIAM J. Matrix Anal. Appl.， SIAM J. Numer. Anal.，SIAM J. Sci. Comput.等国际顶级学术期刊上发表学术论文20余篇。
报告摘要：
       In this paper, we consider the inverse eigenvalue problem for the positive doubly stochasticmatrices,which aims to construct a positive doubly stochastic matrix from the prescribedrealizable spectral data. By using the real Schur decomposition, the inverse problem is written as nonlinear matrix equation on a matrix product manifold. We propose monotone, nonmonotone Riemannian inexact Newton-CG methods for solving the nonlinear matrix equation. The global   and quadratic convergence  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, wereport some numerical tests, including an application in digraph, to illustrate the effectiveness of the proposed methods.