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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 = (). In essence, given the value of A ( h ) {\displaystyle A(h)} for several values of h {\displaystyle h} , we can estimate A ∗ {\displaystyle A^{\ast }} by extrapolating the ...
After trapezoid rule estimates are obtained, Richardson extrapolation is applied. For the first iteration the two piece and one piece estimates are used in the formula 4 × (more accurate) − (less accurate) / 3 . The same formula is then used to compare the four piece and the two piece estimate, and likewise for the higher estimates
In numerical analysis, the Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified midpoint method, [1] to obtain numerical solutions to ordinary ...
Methods based on Richardson extrapolation, [14] such as the Bulirsch–Stoer algorithm, [15] [16] are often used to construct various methods of different orders. Other desirable features include: dense output: cheap numerical approximations for the whole integration interval, and not only at the points t 0, t 1, t 2, ...
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 ...
Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson in his work dated 1910. It is similar to the Jacobi and Gauss–Seidel method. We seek the solution to a set of linear equations, expressed in matrix terms as
Download as PDF; Printable version; In other projects ... This technique is called Richardson extrapolation. ... The above prediction formula is plausible in a sense ...
Richardson extrapolation; Shanks transformation — similar to Aitken's delta-squared process, but applied to the partial sums; Van Wijngaarden transformation — for accelerating the convergence of an alternating series; Abramowitz and Stegun — book containing formulas and tables of many special functions