ncku-talk2009-10-30

NCTS(South)/ NCKU Math Colloquium

DATE 2009-10-30　15:10-16:00

PLACE R204,2F,NCTS,NCKU

SPEAKER Prof. Tsung-Min Hwang (黃聰明教授)（國立台灣師範大學數學系）

TITLE Efficient Solvers for Polynomial and Generalized Eigenvalue Problems Arising in Quantum Dot Simulations

ABSTRACT Jacobi-Davidson type methods are competitive polynomial eigenvalue problem solvers for identifying interior eigenvalues and the corresponding eigenvectors. While the methods can be extended to higher order polynomial eigenvalue problems rather straightforwardly from the linear and generalized cases, it remains indefinite how variants of the Jacobi-Davidson methods perform on polynomial eigenvalue problems arising in real applications. We fulfill the gap partially by proposing several various schemes for solving the correction equations in the Jacobi-Davidson method, deriving a set of polynomial eigenvalue benchmark problems, and conducting numerical experiments to investigate the performance of the methods against the test problems. We find that the scheme involving only one linear system in the iterative solver for the correction equation performs the best.

NCTS(South)/ NCKU Math Colloquium

DATE	2009-10-30　15:10-16:00

PLACE	R204,2F,NCTS,NCKU

SPEAKER	Prof. Tsung-Min Hwang (黃聰明教授)（國立台灣師範大學數學系）

TITLE	Efficient Solvers for Polynomial and Generalized Eigenvalue Problems Arising in Quantum Dot Simulations

ABSTRACT	Jacobi-Davidson type methods are competitive polynomial eigenvalue problem solvers for identifying interior eigenvalues and the corresponding eigenvectors. While the methods can be extended to higher order polynomial eigenvalue problems rather straightforwardly from the linear and generalized cases, it remains indefinite how variants of the Jacobi-Davidson methods perform on polynomial eigenvalue problems arising in real applications. We fulfill the gap partially by proposing several various schemes for solving the correction equations in the Jacobi-Davidson method, deriving a set of polynomial eigenvalue benchmark problems, and conducting numerical experiments to investigate the performance of the methods against the test problems. We find that the scheme involving only one linear system in the iterative solver for the correction equation performs the best.