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In numerical analysis, Aitken's delta-squared process or Aitken extrapolation is a series acceleration method used for accelerating the rate of convergence of a sequence. It is named after Alexander Aitken, who introduced this method in 1926. [1]
Commonly available programs for calculators include everything from math/science related problem solvers to video games, as well as so-called demos. Much of this code is user-created freeware or even open source, though commercial software, particularly for educational and science/engineering markets, is also available. Programmable calculators ...
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 ...
The source code for the Microsoft Windows version of the 2000 video game Monopoly was leaked in August 2018. [178] [179] Mortal Kombat II: 1993 2022 Arcade Fighting: Midway Games: During October 25–27, 2022, Jason Scott uploaded to GitHub 13 repositories containing source code for a variety of video games, including the arcade version of ...
MIT/Public-domain software—Proprietary (engine/game code) Love Conquers All Games Developed using the Ren'Py engine, the game code for Analogue: A Hate Story was released on May 4, 2013 under a public-domain-equivalent license. The source code release includes the entire script of the game for context, but the script remains proprietary. [245]
The sequence produced by other choices of c can be written as a simple function of the sequence when c=1. [1]: 11 Specifically, if Y is the prototypical sequence defined by Y 0 = 0 and Y n+1 = aY n + 1 mod m, then a general sequence X n+1 = aX n + c mod m can be written as an affine function of Y:
Like any series, an alternating series is a convergent series if and only if the sequence of partial sums of the series converges to a limit. The alternating series test guarantees that an alternating series is convergent if the terms a n converge to 0 monotonically , but this condition is not necessary for convergence.
The most-common visualization of the Recamán's sequence is simply plotting its values, such as the figure seen here. On January 14, 2018, the Numberphile YouTube channel published a video titled The Slightly Spooky Recamán Sequence, [3] showing a visualization using alternating semi-circles, as it is shown in the figure at top of this page.