题目：Eigenvalue Calculations in Quantum Many-Body Physics
报告人简介：Weiguo Gao received the B.Sc. and M.Sc. degrees in computational mathematics from Jilin University in 1991 and 1994, respectively, and the Ph.D. degree in computational mathematics from Fudan University in 1997. And then he joined the faculty of Fudan University. He held a visiting professor position in the Computational Research Division at the Lawrence Berkeley National Laboratory for the period 2003-2005. He is currently a professor with the School of Mathematical Sciences and School of Data Science at Fudan University. His research interests are in the area of numerical linear algebra and high performance computing, including linear and nonlinear eigenvalue problems, large scale scientific computing, electronic structure and transition state calculations, numerical methods for data science.
Abstract: 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.