Search results
Results from the WOW.Com Content Network
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.
Some authors use the term Gaussian elimination to refer only to the procedure until the matrix is in echelon form, and use the term Gauss–Jordan elimination to refer to the procedure which ends in reduced echelon form. The name is used because it is a variation of Gaussian elimination as described by Wilhelm Jordan in 1888. However, the ...
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.
In this case it is faster (and more convenient) to do an LU decomposition of the matrix A once and then solve the triangular matrices for the different b, rather than using Gaussian elimination each time. The matrices L and U could be thought to have "encoded" the Gaussian elimination process.
At any step in a Gauss-Seidel iteration, solve the first equation for in terms of , …,; then solve the second equation for in terms of just found and the remaining , …,; and continue to . Then, repeat iterations until convergence is achieved, or break if the divergence in the solutions start to diverge beyond a predefined level.
Gaussian algorithm may refer to: Gaussian elimination for solving systems of linear equations; Gauss's algorithm for Determination of the day of the week; Gauss's method for preliminary orbit determination; Gauss's Easter algorithm; Gauss separation algorithm
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.
Thus, Gauss–Jacobi quadrature can be used to approximate integrals with singularities at the end points. Gauss–Legendre quadrature is a special case of Gauss–Jacobi quadrature with α = β = 0. Similarly, the Chebyshev–Gauss quadrature of the first (second) kind arises when one takes α = β = −0.5 (+0.5).