In numerical analysis, Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of...
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observations, but extrapolation is subject to greater uncertainty and a higher risk of producing meaningless results. Extrapolation may also mean extension...
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f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx} by applying Richardson extrapolation repeatedly on the trapezium rule or the rectangle rule (midpoint...
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Energy cascade War cycles Magnetic helicity Richardson extrapolation Richardson number Modified Richardson iteration Richards equation Multiscale turbulence...
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Numerical integration (section Extrapolation methods)
extrapolating the result from two or more nonzero step sizes, using series acceleration methods such as Richardson extrapolation. The extrapolation function...
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which is equivalent to the Richardson iteration by making t = ω {\displaystyle t=\omega } . Richardson extrapolation Richardson, L.F. (1910). "The approximate...
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Aitken's delta-squared process (redirect from Aitken extrapolation)
print("The last computed extrapolate was ", aitkenX) end Rate of convergence Limit of a sequence Fixed point iteration Richardson extrapolation Sequence transformation...
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C., & Zaglia, M. R. (2013). Extrapolation methods: theory and practice. Elsevier. Monroe, J. L. (2002). Extrapolation and the Bulirsch-Stoer algorithm...
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by heavy numeric computation. He used Richardson extrapolation in 1695, about 200 years earlier than Richardson. He also computated 41 digits of π {\displaystyle...
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evaluated to high precision from a small number of terms using Richardson extrapolation or the Euler–Maclaurin formula. This series can also be transformed...
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Methods of computing square roots Newton's method in optimization Richardson extrapolation Root-finding algorithm Secant method Steffensen's method Subgradient...
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which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified...
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linearly converging sequences Minimum polynomial extrapolation — for vector sequences Richardson extrapolation Shanks transformation — similar to Aitken's...
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15 years earlier than Euler. He used Richardson extrapolation in 1695, about 200 years earlier than Richardson. He also computed 41 digits of π, based...
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places in 1654 using a slightly different method equivalent to Richardson extrapolation. The calculation of π was revolutionized by the development of...
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the integrand is a polynomial of degree three or lower. Using Richardson extrapolation, the more accurate Simpson estimate S ( a , m ) + S ( m , b ) {\displaystyle...
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hence higher density regions are more highly resolved) or based on Richardson extrapolation. All tagged cells are then refined, meaning that a finer grid is...
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expanding the left-hand side in a Taylor series. Alternatively, apply Richardson extrapolation to the central difference approximation to f ′ ( x ) {\displaystyle...
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PDEs High order difference approximations via Taylor series and Richardson extrapolation Methods of integration on a uniform mesh: rectangle rule (also...
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1654 Christiaan Huygens Used a geometrical method equivalent to Richardson extrapolation 10 1665 Isaac Newton 16 1681 Takakazu Seki 11 16 1699 Abraham Sharp...
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functions and complex numbers. 1722 – Takebe Kenko introduces Richardson extrapolation. 1724 – Abraham De Moivre studies mortality statistics and the...
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be used as highly effective extrapolation methods. A simple nonlinear sequence transformation is the Aitken extrapolation or delta-squared method, A :...
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the integrand were a polynomial of the appropriate degree). See: Richardson extrapolation (see also Romberg's method) Null rules Epsilon algorithm "Local"...
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first third of that interval. Using a technique equivalent to Richardson extrapolation, Huygens was able to shorten the inequalities used in Archimedes's...
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help in reducing the number of steps. This technique is called Richardson extrapolation. Beginning with an initial stepsize of h = b − a {\displaystyle...
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sequences. Aitken's delta-squared process Minimum polynomial extrapolation Richardson extrapolation Series acceleration Steffensen's method Hugh J. Hamilton...
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delta-squared process Anderson acceleration Rate of convergence Richardson extrapolation Sequence transformation Weniger (2003). Bender & Orszag (1999)...
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analysis and especially accelerated numerical methods, making use of Richardson extrapolation . He obtained his Candidate degree at Moscow State University in...
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numerically by the Rayleigh–Ritz method. Adding more vectors, see, e.g., Richardson extrapolation, does not result in significant acceleration but increases computation...
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Interior reconstruction (section Extrapolation method)
Prediction interval Regression analysis Richardson extrapolation Static analysis Trend estimation Interpolation Extrapolation domain analysis Dead reckoning Image...
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