Locally supported kernels for spherical spline interpolation

Journal of Approximation Theory

Volumn 89, Issue 2, 1997, Pages 172-194

  Schreiner, Michael ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031142659     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1997.3037     Document Type: Article

References (27)

1. Andrews L. C. Special Functions for Engineers and Applied Mathematicians. 1985;Maxmillian, New York.
2. Aronszajn N. Theory of reproducing kernels. Trans. Amer. Math. Soc. 68:1950;337-404.
3. Berens H., Butzer P. L., Pawelke S. Limitierungsverfahren mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten. Publ. Res. Inst. Math. Sci. Ser. A. 1968;201-268.
4. Bochner S. Positive zonale functions on spheres. Proc. Nat. Acad. Sci. U.S.A. 40:1954;1141-1147.
5. Calderon A. P., Zygmund A. On a problem of mihlin. Trans. Amer. Math. Soc. 78:1955;209-224.
6. Davis P. J. Interpolation and Approximation. 1963;Blaisdell Publishing Company, New York, Toronto, London.
7. Freeden W. On spherical spline interpolation and approximation. Math. Methods Appl. Sci. 3:1981;551-575.
8. Freeden W. A spline interpolation method for solving boundary value problems of potential theory from discretely given data. Numer. Methods Partial Differential Equations. 3:1987;375-398.
9. Freeden W. Spherical spline approximation and its application in physical geodes. Vogel A., Ofeagbu C. O., Gorenflo R., Ursin B. Geophysical Data Inversion Methods and Applications. 1990;Vieweg Publication.
10. Freeden W., Gervens T., Mason J. C. A minimum norm interpolation method for determining the displacement field of a homogeneous isotropic elastic body from discrete data. IMA J. Appl. Math. 44:1990;55-76.
11. Freeden W., Gervens T., Schreiner M. Tensor spherical harmonics and tensor spherical splines. Manuscr. Geod. 19:1994;70-100.
12. Freeden W., Schreiner M. Non-orthogonal expansions on the sphere. Math. Methods Appl. Sci. 18:1995;83-120.
13. Gronwall T. On the degree of convergence of Laplace series. Trans. Amer. Math. Soc. 15:1914;1-30.
14. Magnus W., Oberhettinger F., Soni R. P. Special Functions of Mathematical Physics. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen. Bd. 52:1966;Springer-Verlag, Berlin, Heidelberg, New York.
15. Micchelli C. Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constr. Approx. 2:1986;11-22.
16. Müller C. Spherical Harmonics. Lecture Notes in Mathematics. 17:1966;Springer-Verlag, Berlin, Heidelberg, New York.
17. Powell M. J. D. The theory of radial basis function approximation in 1990. Light W. A. Advances in Numerical Analysis. 1992;Clarendon Press.
18. Rummel R. Satellite gradiometry. Sünkel H. Lecture Notes in Earth Sciences 7, Mathematical and Numerical Techniques in Physical Geodesy. 1986;Springer, Berlin.
19. F. Schneider, 1994, Spherical Splines With Local Supports and Their Application to Scattered Data Distribution, Geomathematics Group, University of Kaiserslautern.
20. Schoenberg I. J. Positive definite functions on spheres. Duke Math. J. 9:1942;96-108.
21. M. Schreiner, 1994, Tensor Spherical Harmonics and Their Application in Satellite Gradiometry, Geomathematics Group, University of Kaiserslautern.
22. Shure L., Parker R. L., Backus, G. E. Harmonic splines for geomagnetic modelling. Phys. Earth Planet. Inter. 28:1982;215-229.
23. Szegö G. Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. 23:1959;Amer. Math. Soc. Providence.
24. Wahba G. Spline interpolation and smoothing on the sphere. SIAM J. Sci. Stat. Comput. 2:1981;5-16.
25. SIAM J. Sci. Stat. Comput. 3:1982;385-386.
26. Wahba G. Surface fitting with scattered noisy data on Euclideand. Rocky Mountain J. Math. 14:1984;281-299.
27. Xu Y., Cheney, E. W. Strictly positive definite functions on spheres. Proc. Amer. Math. Soc. 116:1992;977-981.