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Abstract

The radial basis function (RBF) and quasi Monte Carlo (QMC) methods are two very promising schemes to handle high-dimension problems with complex and moving boundary geometry due to the fact that they are independent of dimensionality and inherently meshless. The two strategies are seemingly irrelevant and are so far developed independently. The former is largely used to solve partial differential equations (PDE), neural network, geometry generation, scattered data processing with mathematical justifications of interpolation theory [1], while the latter is often employed to evaluate high-dimension integration with the Monte Carlo method (MCM) background [2]. The purpose of this communication is to try to establish their intrinsic relationship on the grounds of numerical integral. The kernel function of integral equation is found the key to construct efficient RBFs. Some significant results on RBF construction, error bound and node placement are also presented. It is stressed that the RBF is here established on integral analysis rather than on the sophisticated interpolation and native space analysis.

Details

1009240
Title
A study on radial basis function and quasi-Monte Carlo methods
Author
Publication title
arXiv.org; Ithaca
Publication year
2002
Publication date
Jul 26, 2002
Section
Mathematics; Mathematical Physics
Publisher
Cornell University Library, arXiv.org
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
 
 
Online publication date
2007-05-23
Milestone dates
2002-07-26 (Submission v1)
Publication history
 
 
   First posting date
23 May 2007
ProQuest document ID
2091331352
Document URL
https://www.proquest.com/working-papers/study-on-radial-basis-function-quasi-monte-carlo/docview/2091331352/se-2?accountid=208611
Full text outside of ProQuest
Copyright
© 2002. This work is published under https://arxiv.org/licenses/assumed-1991-2003/license.html (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2023-08-22
Database
ProQuest One Academic