The computation of long geodesics on the ellipsoid by non-series expanding procedure
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- Saito, T. Bull. Geodesique (1970) 98: 341. doi:10.1007/BF02522166
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In this paper the author shows a procedure to settle the computation of very long geodesic lines on the ellipsoid without using the series expansion. The integration of elliptic integrals appearing in the procedure is numerically carried out by means of a mechanical quadrature-the method of Repeated Interval Halving.
The author also devises formulae for the numerical solution of the problem, in order to make the amount of significance error least and determine the kind of quadrant for the computation of inverse trigonometric function.
The anti-podal problem for the direct and inverse solution is rigorously solved by this method.