On a Generalization of Neumann Series of Bessel Functions Using Hessenberg Matrices and Matrix Exponentials

A. Koskela, E. Jarlebring

Forskningsoutput: Kapitel i bok/rapport/konferenshandlingKonferensbidragVetenskapligPeer review

Sammanfattning

The Bessel-Neumann expansion (of integer order) of a function $g:\mathbb{C} \rightarrow\mathbb{C}$ corresponds to representing $g$ as a linear combination of basis functions $\phi_0,\phi_1,\ldots$, i.e., $g(z)=\sum_{\ell = 0}^\infty w_\ell \phi_\ell(s)$, where $\phi_i(z)=J_i(z)$, $i=0,\ldots$, are the Bessel functions. In this work, we study an expansion for a more general class of basis functions. More precisely, we assume that the basis functions satisfy an infinite dimensional linear ordinary differential equation associated with a Hessenberg matrix, motivated by the fact that these basis functions occur in certain iterative methods. A procedure to compute the basis functions as well as the coefficients is proposed. Theoretical properties of the expansion are studied. We illustrate that non-standard basis functions can give faster convergence than the Bessel functions.
Originalspråkengelska
Titel på gästpublikationNumerical Mathematics and Advanced Applications ENUMATH 2017
RedaktörerF. Radu, K. Kumar, I. Berre, J. Nordbotten, I. Pop
Antal sidor10
Volym126
FörlagSpringer, Cham
Utgivningsdatum5 jan 2019
Sidor205-214
ISBN (tryckt)978-3-319-96414-0
ISBN (elektroniskt)978-3-319-96415-7
DOI
StatusPublicerad - 5 jan 2019
Externt publiceradJa
MoE-publikationstypA4 Artikel i en konferenspublikation
EvenemangEuropean Conference on Numerical Mathematics and Advanced Applications ENUMATH 2017 - Voss, Norge
Varaktighet: 25 sep 201729 sep 2017

Publikationsserier

NamnLecture Notes in Computational Science and Engineering
FörlagSpringer-Verlag
ISSN (tryckt)1439-7358

Vetenskapsgrenar

  • 111 Matematik

Citera det här

Koskela, A., & Jarlebring, E. (2019). On a Generalization of Neumann Series of Bessel Functions Using Hessenberg Matrices and Matrix Exponentials. I F. Radu, K. Kumar, I. Berre, J. Nordbotten, & I. Pop (Red.), Numerical Mathematics and Advanced Applications ENUMATH 2017 (Vol. 126, s. 205-214). (Lecture Notes in Computational Science and Engineering). Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_17