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Abstract
In this paper, we present new error bounds for the Lanczos method and the shift-and-invert Lanczos method for computing e−τAv for a large sparse symmetric positive semidefinite matrix A. Compared with the existing error analysis for these methods, our bounds relate the convergence to the condition numbers of the matrix that generates the Krylov subspace. In particular, we show that the Lanczos method will converge rapidly if the matrix A is well-conditioned, regardless of what the norm of τA is. Numerical examples are given to demonstrate the theoretical bounds.
Document Type
Article
Publication Date
1-2-2013
Digital Object Identifier (DOI)
http://dx.doi.org/10.1137/11085935X
Funding Information
This research was supported in part by NSF grant DMS-0915062.
Repository Citation
Ye, Qiang, "Error Bounds for the Lanczos Methods for Approximating Matrix Exponentials" (2013). Mathematics Faculty Publications. 10.
https://uknowledge.uky.edu/math_facpub/10
Notes/Citation Information
Published in SIAM Journal on Numerical Analysis, v. 51, no. 1, p. 68-87.
© 2013, Society for Industrial and Applied Mathematics. Unauthorized reproduction of this article is prohibited.
The copyright holder has granted permission for posting the article here.