Search results
Results from the WOW.Com Content Network
A sound choice of which extrapolation method to apply relies on a priori knowledge of the process that created the existing data points. Some experts have proposed the use of causal forces in the evaluation of extrapolation methods. [2] Crucial questions are, for example, if the data can be assumed to be continuous, smooth, possibly periodic, etc.
An example of Richardson extrapolation method in two dimensions. In numerical analysis , Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value A ∗ = lim h → 0 A ( h ) {\displaystyle A^{\ast }=\lim _{h\to 0}A(h)} .
The zeroeth extrapolation, R(n, 0), is equivalent to the trapezoidal rule with 2 n + 1 points; the first extrapolation, R(n, 1), is equivalent to Simpson's rule with 2 n + 1 points. The second extrapolation, R(n, 2), is equivalent to Boole's rule with 2 n + 1 points. The further extrapolations differ from Newton-Cotes formulas.
An early successful extrapolation algorithm for initial value problems was published by Roland Bulirsch and Josef Stoer in 1966. [23] A concrete example in the case of a one-step method of order can illustrate the general procedure of extrapolation. With such a method, the calculated approximation for small step sizes ℎ can be easily ...
In mathematics, minimum polynomial extrapolation is a sequence transformation used for convergence acceleration of vector sequences, due to Cabay and Jackson. [1] While Aitken's method is the most famous, it often fails for vector sequences. An effective method for vector sequences is the minimum polynomial extrapolation.
Two classical techniques for series acceleration are Euler's transformation of series [1] and Kummer's transformation of series. [2] A variety of much more rapidly convergent and special-case tools have been developed in the 20th century, including Richardson extrapolation, introduced by Lewis Fry Richardson in the early 20th century but also known and used by Katahiro Takebe in 1722; the ...
Nearest neighbor interpolation (blue lines) in one dimension on a (uniform) dataset (red points) Nearest neighbor interpolation on a uniform 2D grid (black points). Each colored cell indicates the area in which all the points have the black point in the cell as their nearest black point.
For example, for Newton's method as applied to a function f to oscillate between 0 and 1, it is only necessary that the tangent line to f at 0 intersects the x-axis at 1 and that the tangent line to f at 1 intersects the x-axis at 0. [17] This is the case, for example, if f(x) = x 3 − 2x + 2.