Bulletin géodésique

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

The computation of long geodesics on the ellipsoid through Gaussian quadrature

  • Tsutomu Saito


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.


Azimuth Truncation Error Gaussian Quadrature Computational Error Decimal Digit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  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
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    P.J. DAVIS and P. RABINOWITZ:Methods of Numerical Integration, Academic Press, 1975.Google Scholar
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    R.H. RAPP:Geometric Geodesy, Vol. II (Advanced Technique), 1975, The Ohio State University.Google Scholar
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    H.F. RAINSFORD:Long Geodesics on the Ellipsoid, Bulletin Géodésique,37, pp. 12–21. Septembre 1955.CrossRefGoogle Scholar
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    J. YAMANOUCHIet al,: Numerical Calculus for Computers III, (in Japanese), Baifukan Tokyo, pp. 279–301, 1971.Google Scholar
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    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
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    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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