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数学学科2021系列学术报告之十九

来源:理学院 发布日期:2021-09-17

  报告题目:Smallest Eigenvalue of Large Hankel Matrices at critical point

  报告人:Chen Yang

  报告时间:9月17日(星期五)14:00-15:00

  腾讯会议(ID):685 785 547

  报告摘要:We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. We study a family of Hankel matrices generated by the weight w(x)=exp(x^β), supported on [0, ∞) and β>0. In the situation where β>1/2, the smallest eigenvalue tend to 0, exponentially fast as N gets large. If β<1/2, the situation where the classical moment problem is indeterminate, the smallest eigenvalue is bounded from below by a positive number for all N, including infinity. If β=1/2, it is conjectured that the smallest eigenvalue tends to 0 algebraically, with a precise exponent.

  报告人简介: Chen Yang, received his Phd in the University of Massachusetts, did his Post-Doc at the Cavendish Laboratory, Cambridge University,?University of Karlsruhe,?and the Max Planck Institute, Stuggart, before he joined Imperial College London, in 1992. Chen become Professor of Mathematical Physics in 2004,? then he moved to the University of Macau in 2012?as Professor of Mathematics. He works in Random Matrix Theory and problems related to integrable systems.