Sampling inequalities for infinitely smooth radial basis functions and its application to error estimates

Mun Bae Lee; Jungho Yoon

doi:10.1016/j.aml.2014.05.001

Sampling inequalities for infinitely smooth radial basis functions and its application to error estimates

Mun Bae Lee, Jungho Yoon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Recently, Rieger and Zwicknagl (2010) have introduced sampling inequalities for infinitely smooth functions to derive Sobolev-type error estimates. They introduced exponential convergence orders for functions within the native space associated with the given radial basis function (RBF). Our major concern of this paper is to extend the results made in Rieger and Zwicknagl (2010). We derive generalized sampling inequalities for the larger class of infinitely smooth RBFs, including multiquadrics, inverse multiquadrics, shifted surface splines and Gaussians.

Original language	English
Pages (from-to)	40-45
Number of pages	6
Journal	Applied Mathematics Letters
Volume	36
DOIs	https://doi.org/10.1016/j.aml.2014.05.001
State	Published - Oct 2014

Keywords

(Inverse) multiquadrics
Approximation order
Gaussian
Sampling inequality
Shifted surface spline

Access to Document

10.1016/j.aml.2014.05.001

Cite this

@article{c7914d914e31486b9aa412e2a43188d3,

title = "Sampling inequalities for infinitely smooth radial basis functions and its application to error estimates",

abstract = "Recently, Rieger and Zwicknagl (2010) have introduced sampling inequalities for infinitely smooth functions to derive Sobolev-type error estimates. They introduced exponential convergence orders for functions within the native space associated with the given radial basis function (RBF). Our major concern of this paper is to extend the results made in Rieger and Zwicknagl (2010). We derive generalized sampling inequalities for the larger class of infinitely smooth RBFs, including multiquadrics, inverse multiquadrics, shifted surface splines and Gaussians.",

keywords = "(Inverse) multiquadrics, Approximation order, Gaussian, Sampling inequality, Shifted surface spline",

author = "Lee, {Mun Bae} and Jungho Yoon",

note = "Funding Information: The authors are grateful to the anonymous referees for the valuable suggestions on this paper. Jungho Yoon was supported by Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology . ",

year = "2014",

month = oct,

doi = "10.1016/j.aml.2014.05.001",

language = "English",

volume = "36",

pages = "40--45",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier Ltd.",

}

TY - JOUR

T1 - Sampling inequalities for infinitely smooth radial basis functions and its application to error estimates

AU - Lee, Mun Bae

AU - Yoon, Jungho

N1 - Funding Information: The authors are grateful to the anonymous referees for the valuable suggestions on this paper. Jungho Yoon was supported by Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology .

PY - 2014/10

Y1 - 2014/10

N2 - Recently, Rieger and Zwicknagl (2010) have introduced sampling inequalities for infinitely smooth functions to derive Sobolev-type error estimates. They introduced exponential convergence orders for functions within the native space associated with the given radial basis function (RBF). Our major concern of this paper is to extend the results made in Rieger and Zwicknagl (2010). We derive generalized sampling inequalities for the larger class of infinitely smooth RBFs, including multiquadrics, inverse multiquadrics, shifted surface splines and Gaussians.

AB - Recently, Rieger and Zwicknagl (2010) have introduced sampling inequalities for infinitely smooth functions to derive Sobolev-type error estimates. They introduced exponential convergence orders for functions within the native space associated with the given radial basis function (RBF). Our major concern of this paper is to extend the results made in Rieger and Zwicknagl (2010). We derive generalized sampling inequalities for the larger class of infinitely smooth RBFs, including multiquadrics, inverse multiquadrics, shifted surface splines and Gaussians.

KW - (Inverse) multiquadrics

KW - Approximation order

KW - Gaussian

KW - Sampling inequality

KW - Shifted surface spline

UR - http://www.scopus.com/inward/record.url?scp=84902169100&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2014.05.001

DO - 10.1016/j.aml.2014.05.001

M3 - Article

AN - SCOPUS:84902169100

SN - 0893-9659

VL - 36

SP - 40

EP - 45

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Sampling inequalities for infinitely smooth radial basis functions and its application to error estimates

Abstract

Keywords

Access to Document

Fingerprint

Cite this