New matrix function approximations and quadrature rules based on the Arnoldi process
- The Arnoldi process can be applied to inexpensively approximate matrix functions of the form f (A)v and matrix functionals of the form v*(f (A))*g(A)v, where A is a large square non-Hermitian matrix, v is a vector, and the superscript * denotes transposition and complex conjugation. Here f and g are analytic functions that are defined in suitable regions in the complex plane. This paper reviews available approximation methods and describes new ones that provide higher accuracy for essentially the same computational effort by exploiting available, but generally not used, moment information. Numerical experiments show that in some cases the modifications of the Arnoldi decompositions proposed can improve the accuracy of v*(f (A))*g(A)v about as much as performing an additional step of the Arnoldi process.
| Verfasserangaben: | Nasim Eshghi, Thomas MachORCiDGND, Lothar ReichelGND |
|---|---|
| DOI: | https://doi.org/10.1016/j.cam.2021.113442 |
| ISSN: | 0377-0427 |
| ISSN: | 1879-1778 |
| Titel des übergeordneten Werks (Englisch): | Journal of computational and applied mathematics |
| Verlag: | Elsevier |
| Verlagsort: | Amsterdam |
| Publikationstyp: | Wissenschaftlicher Artikel |
| Sprache: | Englisch |
| Datum der Erstveröffentlichung: | 01.08.2021 |
| Erscheinungsjahr: | 2021 |
| Datum der Freischaltung: | 25.04.2024 |
| Freies Schlagwort / Tag: | Arnoldi process; Matrix function approximation; Quadrature rule |
| Band: | 391 |
| Aufsatznummer: | 113442 |
| Seitenanzahl: | 12 |
| Fördernde Institution: | NSF, USANational Science Foundation (NSF) [DMS-1720259] |
| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer Review: | Referiert |
