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In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps:
Mehrotra's predictor–corrector method in optimization is a specific interior point method for linear programming.It was proposed in 1989 by Sanjay Mehrotra. [1]The method is based on the fact that at each iteration of an interior point algorithm it is necessary to compute the Cholesky decomposition (factorization) of a large matrix to find the search direction.
A prediction line must be constructed based on the right end point tangent's slope alone, approximated using Euler's Method. If this slope is passed through the left end point of the interval, the result is evidently too steep to be used as an ideal prediction line and overestimates the ideal point.
The application of MacCormack method to the above equation proceeds in two steps; a predictor step which is followed by a corrector step. Predictor step: In the predictor step, a "provisional" value of u {\displaystyle u} at time level n + 1 {\displaystyle n+1} (denoted by u i p {\displaystyle u_{i}^{p}} ) is estimated as follows
It is a variant of the Verlet integration method. It produces identical positions, but uses a different formula for the velocities. Beeman in 1976 published [2] a class of implicit (predictor–corrector) multi-step methods, where Beeman's method is the direct variant of the third-order method in this class.
Download as PDF; Printable version; In other projects Wikimedia Commons; ... Mehrotra predictor–corrector method; Method of moving asymptotes; Minimax; Mirror descent;
Download as PDF; Printable version ... a trapezoidal predictor-corrector method. ... to convergence in the algorithm but instead to the step size and the core method ...
The Adams–Moulton methods are solely due to John Couch Adams, like the Adams–Bashforth methods. The name of Forest Ray Moulton became associated with these methods because he realized that they could be used in tandem with the Adams–Bashforth methods as a predictor-corrector pair (Moulton 1926); Milne (1926) had the same idea.