Norms of inverses and condition numbers for matrices associated with scattered data
Journal of Approximation Theory
Bounds on multivariate polynomials and exponential error estimates for multiquadratic interpolation
Journal of Approximation Theory
On power functions and error estimates for radial basis function interpolation
Journal of Approximation Theory
The approximation power of moving least-squares
Mathematics of Computation
Improved error bounds for scattered data interpolation by radial basis functions
Mathematics of Computation
Interpolation by radial basis functions on Sobolev space
Journal of Approximation Theory
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Error estimate in fractional differential equations using multiquadratic radial basis functions
Journal of Computational and Applied Mathematics
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The accuracy of interpolation by a radial basis function φ is usually very satisfactory provided that the approximant f is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function φ, no approximation power has yet been established. Hence, the purpose of this study is to discuss the Lp-approximation order (1 ≤ p ≤ ∞) of interpolation to functions in the Sobolev space Wpk(Ω) with k max(0,d/2 - d/p). We are particularly interested in using the "shifted" surface spline, which actually includes the cases of the multiquadric and the surface spline. Moreover, we show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met.