Sampling inequalities for infinitely smooth radial basis functions and its application to error estimates
- 주제(키워드) Radial basis function networks , Approximation orders , Exponential convergence , Gaussians , Generalized samplings , ITS applications , Multiquadrics , Radial Basis Function(RBF) , Radial basis functions , Image segmentation
- 관리정보기술 faculty
- 등재 SCOPUS
- 발행기관 Elsevier Ltd
- 발행년도 2014
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000096616
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.aml.2014.05.001
초록/요약
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.
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