Identification

Title

Locality properties of radial basis function expansion coefficients for equispaced interpolation

Abstract

Many types of radial basis functions (RBFs) are global in terms of having large magnitude across the entire domain. Yet, in contrast, e.g. with expansions in orthogonal polynomials, RBF expansions exhibit a strong property of locality with regard to their coefficients. That is, changing a single data value mainly affects the coefficients of the RBFs which are centred in the immediate vicinity of that data location. This locality feature can be advantageous in the development of fast and well-conditioned iterative RBF algorithms. With this motivation, we employ here both analytical and numerical techniques to derive the decay rates of the expansion coefficients for cardinal data, in both 1D and 2D. Furthermore, we explore how these rates vary in the interesting high-accuracy limit of increasingly flat RBFs.

Resource type

document

Resource locator

Unique resource identifier

code

http://n2t.net/ark:/85065/d7p84c1m

codeSpace

Dataset language

eng

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geoscientificInformation

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Text

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title

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reference date

date type

publication

effective date

2016-01-01T00:00:00Z

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publication

effective date

2008-01-01T00:00:00Z

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None

Responsible organisations

Responsible party

contact position

OpenSky Support

organisation name

UCAR/NCAR - Library

full postal address

PO Box 3000

Boulder

80307-3000

email address

opensky@ucar.edu

web address

http://opensky.ucar.edu/

name: homepage

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pointOfContact

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