Bulletin géodésique

, Volume 53, Issue 2, pp 165–177 | Cite as

The computation of long geodesics on the ellipsoid through Gaussian quadrature

  • Tsutomu Saito
Article

Abstract

Formulas for computing geodesics on the bi-axial ellipsoid through Gaussian quadrature are shown; the estimation of computational errors, truncation and roundoff errors, for the quadrature is carried out; and test examples found in [3] together with those which consist of near anti-podal points on the neighborhood of the equator, are computed with the evaluation of the computational errors.

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References

  1. [1]
    T. SAITO:The Computation of Long Geodesics on the Ellipsoid by Non-Series Expanding Procedure, Bulletin Géodésique,98, pp. 341–374, Décembre 1970.CrossRefGoogle Scholar
  2. [2]
    P.J. DAVIS and P. RABINOWITZ:Methods of Numerical Integration, Academic Press, 1975.Google Scholar
  3. [3]
    R.H. RAPP:Geometric Geodesy, Vol. II (Advanced Technique), 1975, The Ohio State University.Google Scholar
  4. [4]
    H.F. RAINSFORD:Long Geodesics on the Ellipsoid, Bulletin Géodésique,37, pp. 12–21. Septembre 1955.CrossRefGoogle Scholar
  5. [5]
    J. YAMANOUCHIet al,: Numerical Calculus for Computers III, (in Japanese), Baifukan Tokyo, pp. 279–301, 1971.Google Scholar
  6. [6]
    T. VINCENTY:Direct and inverse Solutions of Geodesics with the Application of Nested Equations, Survey Review No. 176, 1975 and his letters to the author.Google Scholar
  7. [7]
    S.D. CONTE:Elementary Numerical Analysis, McGraw-Hill Book Company, 1965, p. 84. p. 19, and p. 25.Google Scholar

Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1979

Authors and Affiliations

  • Tsutomu Saito
    • 1
  1. 1.Construction CollegeKodaira-shi TokyoJapan

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