Reliable computation of exterior eigenvalues through matrix functions

Speaker:    Fei Xue, Clemson University

Time:         09:00-10:00 , Mar.04

Location:   SIST 2-415

Host:         Qifeng Liao

Abstract:

Exterior eigenvalues of large sparse matrices are needed for various applications, such as linear stability analysis. These eigenvalues are difficult to compute efficiently and reliably if they are much smaller than the dominant eigenvalues in modulus. Traditional spectral transformations such as Cayley transform are far from reliable. In this talk, we discuss a simple idea of spectral transformation based on functions of matrices that maps the desired exterior eigenvalues to dominant ones. Approximations of the action of matrix functions on vectors is fundamental for this approach, which can be performed by rational Krylov subspace methods (RKSM). Numerical experiments for linear and nonlinear eigenvalue problems demonstrate the reliability of this method.

Bio:

B.E. & M.E - Southeast University, China, 2001 & 2004. Ph.D - University of Maryland College Park, 2009, advisor is Howard Elman. Research Assistant Professor at Temple University 2009-2012, with Daniel Szyld. Then Assistant Professor at Universty of Louisiana at Lafayette 2012-2016. Assistant Professor at Clemson University 2016-2018, and Associate Professor 2018-now.