منابع مشابه
On interpolation by radial polynomials
A lemma of Micchelli’s, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback’s more recent extension of this lemma and Schaback’s result concerning interpolation by radial polynomials. Schaback’s interpolant is explored. In his most-cited paper, [M], Micchelli supplies the following interesting auxiliary lemma (h...
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In many cases, multivariate interpolation by smooth radial basis functions converges towards polynomial interpolants, when the basis functions are scaled to become “wide”. In particular, examples show that interpolation by scaled Gaussians seems to converge towards the de Boor/Ron “least” polynomial interpolant. The paper starts by providing sufficient criteria for the convergence of radial int...
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Abstract. We explore a connection between Gaussian radial basis functions and polynomials. Using standard tools of potential theory, we find that these radial functions are susceptible to the Runge phenomenon, not only in the limit of increasingly flat functions, but also in the finite shape parameter case. We show that there exist interpolation node distributions that prevent such phenomena an...
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Interpolation by translates of suitable radial basis functions is an important approach towards solving the scattered data problem. However, for a large class of smooth basis functions (including multiquadrics f(x)=(|x|+l), m > d/2, 2m−d ̈ 2Z), the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximands. The approximands f need to b...
متن کاملOn the Eeciency of Interpolation by Radial Basis Functions
We study the computational complexity, the error behavior, and the numerical stability of interpolation by radial basis functions. It turns out that these issues are intimately connected. For the case of compactly supported radial basis functions, we consider the possibility of getting reasonably good reconstructions of d-variate functions from N data at O(Nd) computational cost and give some s...
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ژورنال
عنوان ژورنال: Advances in Computational Mathematics
سال: 2006
ISSN: 1019-7168,1572-9044
DOI: 10.1007/s10444-004-7630-3