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.
| Author details: | Nasim Eshghi, Thomas MachORCiDGND, Lothar ReichelGND |
|---|---|
| DOI: | https://doi.org/10.1016/j.cam.2021.113442 |
| ISSN: | 0377-0427 |
| ISSN: | 1879-1778 |
| Title of parent work (English): | Journal of computational and applied mathematics |
| Publisher: | Elsevier |
| Place of publishing: | Amsterdam |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/08/01 |
| Publication year: | 2021 |
| Release date: | 2024/04/25 |
| Tag: | Arnoldi process; Matrix function approximation; Quadrature rule |
| Volume: | 391 |
| Article number: | 113442 |
| Number of pages: | 12 |
| Funding institution: | NSF, USANational Science Foundation (NSF) [DMS-1720259] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
