Skip to main content
SpringerLink
Log in

Uniform approximation by spherical spline interpolation

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Aronszjain, N.: Theory of reproducing kernels. Trans. Am. Math. Soc.68, 337–404 (1950)

    Google Scholar 

  2. Dongarra, J.J., Bunch, J.R., Moler, C.B., Stewart, G.W.: LINPACK Users' Guide. SIAM, Philadelphia 1979

    Google Scholar 

  3. Euler, H.J., Groten, E., Hausch, W., Stock, B.: Precise geoid computations at moutaineous coastlines in view of vertical datum determinations. Veröffentlichung des Zentralinstituts für Physik der Erde, Akademie der Wiss. der DDR, Nr. 81 Teil I, 109–139 (1985)

    Google Scholar 

  4. Freeden, W.: On integral formulas of the (unit)sphere and their application to numerical computation of integrals. Computing25, 131–146 (1980)

    Google Scholar 

  5. Freeden, W.: On spherical spline interpolation and approximation. Math. Methods Appl. Sci.3, 551–575 (1981)

    Google Scholar 

  6. Freeden, W.: Spherical spline interpolation-basic theory and computational aspects. J. Comput. Appl. Math.11, 367–375 (1984)

    Google Scholar 

  7. Freeden, W., Reuter, R.: Remainder terms in numerical integration formulas on the sphere. ISNM61. In: Multivariate Approximation Theory II. W. Schempp, K. Zeller (eds.), pp. 151–170. Basel Boston Stuttgart: Birkhäuser 1982

    Google Scholar 

  8. Freeden, W., Reuter, R.: Exact computation of spherical harmonics. Computing32, 365–378 (1984)

    Google Scholar 

  9. Gronwall, T.: On the degree of convergence of Laplace's series. Trans. Am. Math. Soc.15, 1–30 (1914)

    Google Scholar 

  10. Hlawka, E.: Gleichverteilung auf Produkten von Sphären. J. Reine Angew. Math.330, 1–43 (1982)

    Google Scholar 

  11. Meinguet, J.: Multivariate interpolation at arbirary points made simple. Z. Angew. Math. Phys.30, 292–304 (1979)

    Google Scholar 

  12. Müller, Cl.: Spherical harmonics. Lecture Notes in Mathematics17, Berlin Heidelberg New York: Springer 1966

    Google Scholar 

  13. Ragozin, D.: Uniform convergence of spherical harmonic expansions. Math. Ann.195, 87–94 (1972)

    Google Scholar 

  14. Reuter, R.: Über Integralformeln der Einheitssphäre und harmonische Splinefunktionen. Veröff. Geod. Inst. Rheinisch-Westf. Techn. Hochschule Aachen, Nr. 33 (1982)

  15. Schoenberg, I.J.: On trigonometric spline interpolation. J. Math. Mech.13, 795–825 (1964)

    Google Scholar 

  16. Yamabe, H.: On an extension of the Helly's theorem. Osaka J. Math.2, 15–17 (1950)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Reine und Angewandte Mathematik, Rheinisch-Westfälische TH Aachen, Templergraben 55, D-5100, Aachen, Federal Republic of Germany

    Willi Freeden & Peter Hermann

Authors
  1. Willi Freeden
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Hermann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Freeden, W., Hermann, P. Uniform approximation by spherical spline interpolation. Math Z 193, 265–275 (1986). https://doi.org/10.1007/BF01174336

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01174336

Keywords

Search

Navigation