Journal of applied mathematics & informatics
- Volume 23 Issue 1_2
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- Pages.435-443
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- 2007
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
SOBOLEV TYPE APPROXIMATION ORDER BY SCATTERED SHIFTS OF A RADIAL BASIS FUNCTION
Abstract
An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.