2019
Journal article  Open Access

Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices

Pozza S., Simoncini V.

Arnoldi algorithm  Faber polynomials  Computational Mathematics  Inexact Arnoldi algorithm  Matrix functions  Decay bounds  Software  Computer Networks and Communications  Applied Mathematics  Banded matrices 

This paper derives a priori residual-type bounds for the Arnoldi approximation of a matrix function together with a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay behavior of the entries of functions of banded matrices. Specifically, a priori decay bounds for the entries of functions of banded non-Hermitian matrices will be exploited, using Faber polynomial approximation. Numerical experiments illustrate the quality of the results.

Source: BIT (Nord. Tidskr. Inf-Behandl.) 59 (2019): 969–986. doi:10.1007/s10543-019-00763-6

Publisher: Institutionen for informationsbehandling, Lunds Universitet., Lund, Svezia



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BibTeX entry
@article{oai:it.cnr:prodotti:434144,
	title = {Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices},
	author = {Pozza S. and Simoncini V.},
	publisher = {Institutionen for informationsbehandling, Lunds Universitet., Lund, Svezia},
	doi = {10.1007/s10543-019-00763-6},
	journal = {BIT (Nord. Tidskr. Inf-Behandl.)},
	volume = {59},
	pages = {969–986},
	year = {2019}
}