• Title/Summary/Keyword: Conditionally positive definite function

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IMPROVED STATIONARY $L_p$-APPROXIMATION ORDER OF INTERPOLATION BY CONDITIONALLY POSITIVE DEFINITE FUNCTIONS

  • Yoon, Jung-Ho
    • Journal of applied mathematics & informatics
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    • v.14 no.1_2
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    • pp.365-376
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    • 2004
  • The purpose of this study is to show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met. In particular, as a basis function, we are interested in using a conditionally positive definite function $\Phi$ whose generalized Fourier transform is of the form $\Phi(\theta)\;=\;F(\theta)$\mid$\theta$\mid$^{-2m}$ with a bounded function F > 0.

APPROXIMATION METHOD FOR SCATTERED DATA FROM SHIFTS OF A RADIAL BASIS FUNCTION

  • Yoon, Jung-Ho
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1087-1095
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    • 2009
  • In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.

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