Questions tagged [extrapolation]

For question on extrapolation, the process of estimating, beyond the original observation interval.

n mathematics, extrapolation is the process of estimating, beyond the original observation interval, the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk of producing meaningless results. Extrapolation may also mean extension of a method, assuming similar methods will be applicable. Extrapolation may also apply to human experience to project, extend, or expand known experience into an area not known or previously experienced so as to arrive at a (usually conjectural) knowledge of the unknown

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How can I find which function corresponds to a set of data points?

Suppose I have a set of data points like this: 1;1 2;4 3;9 4;16 5;25 6;36 ... The first column is the input of the function and the second one is the result. I can tell if I look at it that the function here is y = f(x^2). The problem is that the…
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Tool to extrapolate data

I have daily data. 6.5315 4.9240 4.3253 3.9703 3.5932 3.2923 3.0785 3.4432 2.6213 2.4083 2.2602 2.1614 2.1351 2.0412 It looks like exponential function or something similar. Is there tool possibly online that may give extrapolated function or…
Max
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How can I derive the dense output of ode45?

I'm currently looking at the implementation of the Dormand-Prince 5(4) Runge-Kutta algorithm (also known as Dopr5, or ode45) in Numerical Recipes Chapter 17. I understand the integration part, but I have trouble with the dense output function, as it…
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Smoothest function which passes through given points?

I am trying to interpolate/extrapolate on the basis of a known collection of (finitely many) points. I'm wondering if there is a way to formalize this intuitive notion: find a 'smoothest' function which passes through each of the points. Of course…
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Can Wynn's $\epsilon$ algorithm be used for sequence limit?

Let's assume we have a sequence $(a_n)$, which converges to some limit $L = \lim_{n\to\infty} a_n$. However, we are able to calculate only first $N$ terms of the sequence. It is clear that, in general, $L \neq a_N$. Is it possible, however, to use…
user54031
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Is there software that interpolates/extrapolates data using a discrete Fourier?

I've read various methods of Fourier interpolation and extrapolation detailed in articles such as Interpolation and Extrapolation Using a High-Resolution Discrete Fourier Transform—so what I'm wondering is, has anyone actually implemented this…
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Relationship between 2 sinusoidal signal data sets?

I'm trying to relate a near shore tidal signal (point A) to 3 points along a long model boundary (points B C D). I want to possibly have a relationship between B C D with which we can convert A predictions into B C and D. At the moment I'm doing a…
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How to fit a function that depends on several nominal and one real variable?

I have data that map several nominal variables and one real parameter into a real value. For example: ('A', 'left', 'male', 'dog', 1.3459) -> 3.453 ('A', 'top', 'male', 'dog', 6.3459) -> 6.137 ... ('C', 'right', 'female', 'cat', 4.726) -> 1.456 I…
Roman
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Maximum of $\sum_{k=0}^{P} (-1)^{k+P}\binom{P}{k} k^N $ with $P\leq N$

For a combinatorics problem, I would need to identify the value of $P$ that maximizes the function $$\Omega(P) = \sum_{k=0}^{P} (-1)^{k+P}\binom{P}{k} k^N$$ with $P\leq N$. Numerically, I see that the maximum is roughly located at $P=3N/4$, but I…
hugues_myr
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Extrapolate a sum using partial sums at powers of two

In an online textbook for MIT OCW 18.013a, Calculus with Applications, the author uses residue calculus to derive the well-known formula $$\sum_{n>0} n^{-2} = \frac{\pi^2}{6}$$ (See Some Special Tricks) He then writes: You can actually sum the…
awkward
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Fine the value of $P(n+1)$ given values of $P$ from 1 to $n$

$P(x)$ is a polynomial of degree $n$ that satisfies $P(k)=\frac{k}{k+1}$ for $k=0,1,2,3,...,n$. Find $P(n+1)$. What have I tried: I have literally no idea how to do questions of this kind. Also, in general what is the method solving such questions…
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Collective term for interpolation and extrapolation

Is there a collective term for both interpolation and extrapolation? If there is such a term, what is it?
porglezomp
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Finding asymptotes given data

Background: I asked this question on Stack Overflow about how to program in Java or VBA a method to calculate asymptotes given a range of data points. I believe the underlying question would be more appropriate here than on SO - if I understand the…
Sid
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Trapezoid Rule to Simpson's Rule Extrapolation

I need to show that one extrapolation of the trapezoid rule leads to Simpson's rule. I've looked through the other posts on ME, specifically the post with the same title, and this for help, but I still don't have a clear idea of how to answer this.…
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Richardson extrapolation (improve formula)

Use Richardson extrapolation to improve the formula $$ f''(x) \sim \frac{f(x+h)-2f(x)+f(x-h)}{h^2} $$ so that the error is reduced to order $h^4$ I am not sure how to go about doing this problem, if anyone could help it would be much appreciated,…
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