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extrapolation

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extrapolation
extrapolation (ˌɛkstrəpəʊˈleɪʃən) [f. interpolation by the substitution of extra for the first member of the word.] Math. The action or method of finding by a calculation based on the known terms of a series, other terms outside of them, whether preceding or following. Hence transf., the drawing of ... Oxford English Dictionary
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Extrapolation
quadratic extrapolation, etc.). Extrapolation wikipedia.org
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extrapolation
extrapolation/ɪkˌstræpəˈleɪʃn; ɪk`stræpəˌleʃən/ n[U]~ (from sth) (fml 文) He estimated his income tax bill by extrapolation from figures submitted in previous years. 他从前几年的报税数字推算出自己应缴的所得税数额. =>illus at chart见chart之插图. 牛津英汉双解词典
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Extrapolation (journal)
Extrapolation is an academic journal covering speculative fiction, established in 1959. Extrapolation appears three times a year. wikipedia.org
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Extrapolation (album)
Extrapolation is the debut album by English jazz guitarist John McLaughlin. wikipedia.org
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Richardson Extrapolation Suppose that $$ L=\lim_{h\rightarrow 0}f(h) $$ and that $$L-f(h)=c_{6}h^{6}+c_{9}h^{9}+\cdots $$ What combination of f(h) and f(h/2) should be the best estimate of L ?
$L-f(h)=ah^6+bh^9$ $L-f(h/2)=a(h/2)^6+b(h/2)^9$ Now cancel the $a$ term between the two $[L-f(h)]-64[L-f(h/2)]=bh^9-64b(h/2)^9$ $64f(h/2)-f(h)-63L=7b/8h^9$ $L=(64f(h/2)-f(h))/63-b/72h^9$ Hence the best approximation for $L$ from this step of Richardson is $(64f(h/2)-f(h))/63$. You can see that if th...
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Langley extrapolation
Since aerosols tend to be more concentrated at low altitude, Langley extrapolation is often performed at high mountain sites. By extrapolation, researchers determine their performance under space conditions. wikipedia.org
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An extrapolation problem: finding the constant term of a polynomial $f(x)$ is a degree $6$ polynomial and $f(n)=\frac{1}{n}$ when $n=1, 2, 3, 4, 5, 6, 7$. How to find the constant term of $f(x)$?
By the well-known properties of the forward difference operator, if $f$ is a polynomial with degree $\leq 6$ we have $$ \sum_{k=0}^{7}\binom{7}{k}(-1)^k\,f(r+k) = 0 $$ for any $r\in\mathbb{R}$. In our case, by picking $r=0$ and exploiting the binomial theorem we get $$ f(0)=\sum_{k=1}^{7}\binom{7}{k...
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Extrapolation domain analysis
Extrapolation domain analysis (EDA) is a methodology for identifying geographical areas that seem suitable for adoption of innovative ecosystem management To derive the extrapolation domains, Bayesian and frequentist statistical modelling techniques are used. wikipedia.org
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Richardson's Extrapolation Use Richardson's extrapolation to find a 3 point 2nd order approximation of f '(x). I'm not sure how to go about to start this, i'm not the best when using richardson's extrapolation.
From the two-point forward difference formula, we have: $$\tag 1 f'(x) \approx \dfrac{f(x+h)-f(x)}{h}$$ Using Richardson's, we replace $h$ by $\dfrac{h}{2}$ in $(1)$, yielding: $$\tag 2 f'(x) \approx 2\dfrac{f(x+h/2)-f(x)}{h}$$ Subtracting $2 \times (2)$ from $(1)$ (this is to get the Richardson for...
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Minimum polynomial extrapolation
In mathematics, minimum polynomial extrapolation is a sequence transformation used for convergence acceleration of vector sequences, due to Cabay and Jackson An effective method for vector sequences is the minimum polynomial extrapolation. wikipedia.org
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Richardson extrapolation Simpson's rule "Assume that S(h) is equivalent to the (composite) Simpson's rule where h is the size of the step. Correct use of Richardson's extrapolation gives the formula: $R(h) = \frac {16...
Given a method $A(h) = \alpha_0 + \alpha_1 h^k +\mathcal{O}(h^{k+1})$ that approximates $\alpha_0$, the idea is to combine $A$ at varying step sizes to eliminate the lowest power of $h$, say $h^k$. Since the error of Simpson's rule is $\mathcal{O}(h^4)$, we have $S(h) = \alpha_0 + \alpha_1 h^4 + \ma...
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Extrapolation Algorithm Based on the Seven-state ... - co-journal.com
（Army Academy of Artillery and Air Defense, Hefei 230031, Anhui, China） Received:2018-02-27 Revised:2018-02-27 Online:2018-11-19 www.co-journal.com
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UVA326 LA5434 POJ1538 Extrapolation Using a Difference Table【二项式】-爱代码爱编程
Extrapolation Using a Difference TableTime Limit: 1000MS Memory Limit: 10000KTotal Submissions: 306 Accepted: 166DescriptionA very old technique for extrapolating a sequence of values is based on the use of a difference table. The difference table us UVA326 LA5434 POJ1538 Extrapolation Using a Difference Table【二项式】
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Road to the Deep Sky: Richardson extrapolation in BS PDE
吾令羲和弭节兮，望崦嵫而勿迫。 路曼曼其修远兮，吾将上下而求索。 Saturday, October 27, 2007. Richardson extrapolation in BS PDE
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