On the stationary Lp -approximation power to derivatives by radial basis function interpolation

Jungho Yoon

doi:10.1016/j.amc.2003.10.009

On the stationary L_p -approximation power to derivatives by radial basis function interpolation

Jungho Yoon

Department of Mathematics

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

2 Scopus citations

Abstract

In this paper, we consider approximation to derivatives of a function by using radial basis function interpolation. Most of well-known theories for this problem provide error analysis in terms of the so-called native space, say C_φ. However, if a basis function φ is smooth, the space C_φ is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.

Original language	English
Pages (from-to)	875-887
Number of pages	13
Journal	Applied Mathematics and Computation
Volume	150
Issue number	3
DOIs	https://doi.org/10.1016/j.amc.2003.10.009
State	Published - 17 Mar 2004

Keywords

'Shifted' surface spline
Approximation power
Homogeneous Sobolev space
Interpolation
Multiquadric
Radial basis function

Access to Document

10.1016/j.amc.2003.10.009

Cite this

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title = "On the stationary Lp -approximation power to derivatives by radial basis function interpolation",

abstract = "In this paper, we consider approximation to derivatives of a function by using radial basis function interpolation. Most of well-known theories for this problem provide error analysis in terms of the so-called native space, say Cφ. However, if a basis function φ is smooth, the space Cφ is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.",

keywords = "'Shifted' surface spline, Approximation power, Homogeneous Sobolev space, Interpolation, Multiquadric, Radial basis function",

author = "Jungho Yoon",

note = "Funding Information: This work was supported by Korea Research Foundation Grant (KRF-2003-C00014). ",

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AB - In this paper, we consider approximation to derivatives of a function by using radial basis function interpolation. Most of well-known theories for this problem provide error analysis in terms of the so-called native space, say Cφ. However, if a basis function φ is smooth, the space Cφ is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.

KW - 'Shifted' surface spline

KW - Approximation power

KW - Homogeneous Sobolev space

KW - Interpolation

KW - Multiquadric

KW - Radial basis function

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