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New Algorithms for Eigenvalue Calculations

活動(dòng)信息

  • 開(kāi)始時(shí)間:2021-05-09 10:00
  • 活動(dòng)地點(diǎn):創(chuàng)新園大廈A1101
  • 主講人:高衛(wèi)國(guó)

活動(dòng)簡(jiǎn)介

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.

主講人介紹

復(fù)旦大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授 、博士生導(dǎo)師,大數(shù)據(jù)學(xué)院副院長(zhǎng)。計(jì)算物質(zhì)科學(xué)教育部重點(diǎn)實(shí)驗(yàn)室、教育部創(chuàng)新團(tuán)隊(duì)《復(fù)雜物質(zhì)體系的計(jì)算研究》、上海市數(shù)據(jù)科學(xué)重點(diǎn)實(shí)驗(yàn)室成員。《高等學(xué)校計(jì)算數(shù)學(xué)學(xué)報(bào)》《數(shù)值計(jì)算與計(jì)算機(jī)應(yīng)用》編委。主要研究領(lǐng)域?yàn)閿?shù)值線性代數(shù)和高性能計(jì)算,包括線性與非線性特征值問(wèn)題、大規(guī)模科學(xué)與并行計(jì)算、電子結(jié)構(gòu)計(jì)算與鞍點(diǎn)計(jì)算、數(shù)據(jù)科學(xué)中的數(shù)值分析問(wèn)題等。文章發(fā)表在SINUM,SISC,SIMAX,Numer Math,J Comp Phys等計(jì)算數(shù)學(xué)專(zhuān)業(yè)雜志和ACM TOMS,IEEE TAC,Int J Numer Meth Eng,JACS,J Chem Phys,Comput Phys Commun,Comp Mater Sci等應(yīng)用領(lǐng)域雜志上。