# 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

- Mathematics
- 1993

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 in… Expand

On spherical spline interpolation and approximation

- Mathematics
- 1981

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 to… Expand

Modified multiquadric methods for scattered data interpolation over a sphere

- Mathematics, Computer Science
- Comput. Aided Geom. Des.
- 1990

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. Several… Expand

Spherical spline interpolation—basic theory and computational aspects

- Mathematics
- 1984

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 are… Expand

On the Permanence Property in Spherical Spline Interpolation

- Mathematics
- 1982

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 is… Expand

Optimal Smoothing of Noisy Data Using Spline Functions

- Mathematics
- 1981

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 natural… Expand

Spherical Spline Approximation and its Application in Physical Geodesy

- Mathematics
- 1990

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 their… Expand

Locally Supported Kernels for Spherical Spline Interpolation

- Mathematics
- 1997

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 and… Expand

Convergence Rates for Multivariate Smoothing Spline Functions.

- Mathematics
- 1982

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 herein… Expand

Interpolation of data on the surface of a sphere

- Mathematics, Computer Science
- TOMS
- 1984

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