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NOTE: Gauss's method is a preliminary orbit determination, with emphasis on preliminary. The approximation of the Lagrange coefficients and the limitations of the required observation conditions (i.e., insignificant curvature in the arc between observations, refer to Gronchi [2] for more details) causes inaccuracies.
Gauss's method, made famous in his 1801 "recovery" of the first lost minor planet, Ceres, has been subsequently polished. One use is in the determination of asteroid masses via the dynamic method . In this procedure Gauss's method is used twice, both before and after a close interaction between two asteroids.
Carl Friedrich Gauss in 1810 devised a notation for symmetric elimination that was adopted in the 19th century by professional hand computers to solve the normal equations of least-squares problems. [6] The algorithm that is taught in high school was named for Gauss only in the 1950s as a result of confusion over the history of the subject. [7]
Gauss's algorithm for Determination of the day of the week; Gauss's method for preliminary orbit determination; ... additional terms may apply.
This is an accepted version of this page This is the latest accepted revision, reviewed on 28 December 2024. German mathematician, astronomer, geodesist, and physicist (1777–1855) "Gauss" redirects here. For other uses, see Gauss (disambiguation). Carl Friedrich Gauss Portrait by Christian Albrecht Jensen, 1840 (copy from Gottlieb Biermann, 1887) Born Johann Carl Friedrich Gauss (1777-04-30 ...
The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function.
The generalized Gauss–Newton method is a generalization of the least-squares method originally described by Carl Friedrich Gauss and of Newton's method due to Isaac Newton to the case of constrained nonlinear least-squares problems.
Combining two consecutive steps of these methods into a single test, one gets a rate of convergence of 9, at the cost of 6 polynomial evaluations (with Horner's rule). On the other hand, combining three steps of Newtons method gives a rate of convergence of 8 at the cost of the same number of polynomial evaluation.