Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



An application of the multivariate Lagrange-Bürmann expansion in mathematical geodesy

Authors: P. Henrici and G. R. Wilkens
Journal: Quart. Appl. Math. 45 (1987), 165-172
MSC: Primary 86A30
DOI: https://doi.org/10.1090/qam/885178
MathSciNet review: 885178
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the simplified model of geodesy where the earth is conceived as a rotational ellipsoid, if the eccentricity of the ellipsoid is to be determined from gravity measurements, an equation of the form $ y = x - zh\left( x \right)$ is to be solved for $ x$, where $ y$ and $ z$ are small parameters whose values can be measured and $ h$ is a known function. We obtain the expansion of $ x$ in powers of $ y$ and $ z$ by means of the general Lagrange--Bürmann formula.

References [Enhancements On Off] (What's this?)

  • [1] J. C. Alexander, The numerics of computing geodetic ellipsoids, SIAM Rev. 27, 241-247 (1985) MR 792455
  • [2] B. W. Char, K. O. Geddes, G. H. Gonnet, and S. M. Watt, Maple user's manual, 3rd ed., Univ. of Waterloo Res. Rep. CS-83-41 (1983)
  • [3] P. Henrici, Die Lagrange-Bürmannsche Formel bei formalen Potenzreihen, Jber. Deutsch. Math.-Verein. 86, 115-134 (1984) MR 766156
  • [4] W. A. Hieskanen and H. Moritz, Physical geodesy, Freeman, San Francisco, 1966

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 86A30

Retrieve articles in all journals with MSC: 86A30

Additional Information

DOI: https://doi.org/10.1090/qam/885178
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society