A fast numerical method for evaluation of Calderón commutators
Goldberg, M.J. Hrycak, Tomasz Kim, S.
Goldberg, M.J.
Hrycak, Tomasz
Kim, S.
Citations
Altmetric:
Authors
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2003-09-15
Type
Article
Genre
Keywords
Calderón commutators,Cauchy integral,Fast numerical algorithms,Harmonic functions,Laplace equation,Algorithm,Integral equations,Laplace transformation,Nonlinear systems,Perturbation techniques,Multilinear operators,Mathematical operators
Subjects (LCSH)
Citation
Maxim J. Goldberg, Tomasz Hrycak, Seonja Kim, A fast numerical method for evaluation of Calderón commutators, Journal of Computational and Applied Mathematics, Volume 158, Issue 2, 2003, Pages 473-484, ISSN 0377-0427, https://doi.org/10.1016/S0377-0427(03)00483-7.
Abstract
We describe a methodology for fast evaluation of multilinear operators that are generated by a rapidly computable nonlinear operator. We illustrate this idea by developing a simple numerical algorithm for the fast evaluation of Calderón commutators of all orders, C<inf>n</inf>f(x) = p.v. ∫∞ <inf>-∞</inf> (A(x)-A(y))n/(x-y)n+1 f(y) dy, n = 1,2,... . The method is based on a representation of the commutators as derivatives of a one parameter family of real-valued versions of Cauchy integrals. We include numerical experiments for the first two commutators. Additionally, we consider the Dirichlet problem for the Laplacian in the unbounded region above the graph of a function. We demonstrate that Calderón commutators appear as building blocks of the functional coefficients of a perturbative solution for this problem. © 2003 Elsevier B.V. All rights reserved. © 2017 Elsevier B.V., All rights reserved.
Table of Contents
Description
This is an open access article under the CC BY license.
Publisher
Elsevier B.V.
Journal
Journal of Computational and Applied Mathematics
Book Title
Series
Digital Collection
Finding Aid URL
Use and Reproduction
Archival Collection
PubMed ID
ISSN
03770427