New Algorithms for Eigenvalue Calculations


  • 开始时间:2021-05-09 10:00
  • 活动地点:创新园大厦A1101
  • 主讲人:高卫国


In this talk I will present our collaborative work on new algorithms for solving two different types of eigenvalue problems. Firstly, a novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. These algorithms achieve eigenvectors instead of eigenspace. Global convergence and local linear convergence are discussed. Efficiency of new algorithms are demonstrated on random matrices and matrices from computational chemistry. Secondly, we explore the possibility of using a reinforcement learning (RL) algorithm to solve large-scale k-sparse eigenvalue problems. By describing how to represent states, actions, rewards and policies, an RL algorithm is designed and demonstrated the effectiveness on examples from quantum many-body physics.


复旦大学数学科学学院教授 、博士生导师,大数据学院副院长。计算物质科学教育部重点实验室、教育部创新团队《复杂物质体系的计算研究》、上海市数据科学重点实验室成员。《高等学校计算数学学报》《数值计算与计算机应用》编委。主要研究领域为数值线性代数和高性能计算,包括线性与非线性特征值问题、大规模科学与并行计算、电子结构计算与鞍点计算、数据科学中的数值分析问题等。文章发表在SINUM,SISC,SIMAX,Numer Math,J Comp Phys等计算数学专业杂志和ACM TOMS,IEEE TAC,Int J Numer Meth Eng,JACS,J Chem Phys,Comput Phys Commun,Comp Mater Sci等应用领域杂志上。