Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem

Authors:
Zhongming Teng;Ren-Cang Li
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen, 361005, PR China;Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019, United States
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 5
Cited 0

The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems

SIAM Journal on Matrix Analysis and Applications
Applied numerical linear algebra

Applied numerical linear algebra
The symmetric eigenvalue problem

The symmetric eigenvalue problem
Numerical Methods for Electronic Structure Calculations of Materials

SIAM Review
The university of Florida sparse matrix collection

ACM Transactions on Mathematical Software (TOMS)

Quantified Score

Hi-index	7.29

Visualization

Abstract

Two different Lanczos-type methods for the linear response eigenvalue problem are analyzed. The first one is a natural extension of the classical Lanczos method for the symmetric eigenvalue problem while the second one was recently proposed by Tsiper specially for the linear response eigenvalue problem. Our analysis leads to bounds on errors for eigenvalue and eigenvector approximations by the two methods. These bounds suggest that the first method can converge significantly faster than Tsiper's method. Numerical examples are presented to support this claim.