Corpus ID: 17006506

A Survey on Spherical Spline

@inproceedings{Freeden1997ASO,
  title={A Survey on Spherical Spline},
  author={ApproximationbyWilli Freeden and M. Schreiner and R. Franke},
  year={1997}
}
Spline functions that approximate data given on the sphere are developed in a weighted Sobolev space setting. The exibility of the weights makes possible the choice of the approximating function in a way which emphasizes attributes desirable for the particular application area. Examples show that certain choices of the weight sequences yield known methods. A convergence theorem containing explicit constants yields a usable error bound. Our survey ends with the discussion of spherical splines in… Expand
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References

SHOWING 1-10 OF 129 REFERENCES
Generalized Weighted Spline Approximation on the Sphere
Spline functions that interpolate data given on the sphere are developed in a weighted Sobolev space setting. The flexibility of the weights makes possible the choice of the approximating function inExpand
On spherical spline interpolation and approximation
Spherical spline functions are introduced by use of Green's surface functions with respect to the (Laplace-)Beltrami operator of the (unit) sphere. Natural (spherical) spline functions are used toExpand
Modified multiquadric methods for scattered data interpolation over a sphere
Abstract Given arbitrary points on a sphere and associated real values, we address the problem of constructing a smooth function defined over the sphere which interpolates the given data. SeveralExpand
Spherical spline interpolation—basic theory and computational aspects
Abstract The purpose of the paper is to adapt to the spherical case the basic theory and the computational method known from surface spline interpolation in Euclidean spaces. Spline functions areExpand
On the Permanence Property in Spherical Spline Interpolation
Abstract : Spherical spline functions are introduced by use of Green's (surface) functions with respect to the Beltrami operator on the sphere. The method of interpolation by spherical splines isExpand
Optimal Smoothing of Noisy Data Using Spline Functions
We consider the problem of approximating a function f supposed to be “smooth”, given its values known with error at n different points of a real interval $[a,b]$. To approximate f we use the naturalExpand
Spherical Spline Approximation and its Application in Physical Geodesy
Until recently, spherical harmonics have constituted the class of functions used more frequently than others to approximate functions on the (unit) sphere. The basic reason was because of theirExpand
Locally Supported Kernels for Spherical Spline Interpolation
By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is extended, since the resulting interpolation matrix is sparse andExpand
Convergence Rates for Multivariate Smoothing Spline Functions.
Abstract : Smoothing splines are used to approximate smooth functions when there are only available noisy values of the function at discrete values of the independent variables. It is shown hereinExpand
Interpolation of data on the surface of a sphere
  • R. Renka
  • Mathematics, Computer Science
  • TOMS
  • 1984
TLDR
Methods and software that extend the C ~ interpolant of data values associated with arbitrarily distributed nodes on the surface of a sphere method are described and test results are presented. Expand
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