# Questions tagged [extrapolation]

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

99 questions
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### Natural Cubic Spline beyond boundary guarantees constant slope?

my understanding is that for if I have five points, I can interpolate a natural cubic spline out of any five points with increasing x, because degree of freedom is five. But when I try the python ...
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### Propagating Uncertainties on Interpolated Data

I have a data set of 2000 $[x, F(x), \delta F(x)]$ triples, where $x$ is exact and $F$ is a measured value with an uncertainty $\delta F$. I can interpolate/fit the function however needed, and this ...
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### Is filling in grid corners extrapolation or interpolation?

Let's say I measure temperature at locations on a regular 3x5 grid but I am missing data at the 4 grid corners. If I use the available measurements to estimate the grid corner values, am I performing ...
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### Error in Pareto extrapolation of power function

How can we derive error in extrapolation if one tries to extrapolate a power function with Pareto distribution(which in itself is a power function) below a certain threshold?
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### Analytically get amount of points sampled from a polygon extrapolated into another polygon

I am sampling points (x,y) uniformly from a polygon $P_1$ and extrapolating them according to $$\begin{cases} x_{ex} = x + s\cdot \cos (h) \\ y_{ex} = y + s\cdot \sin (h) \end{cases}$$ where $s$ is ...
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### Numerical Analysis - $n$-sided polygon tangential

i need help with this question..I'm not so sure how to go about the arguments. Any help would be appreciated. Consider a regular $n$-sided polygon tangential to and enclosing the unit circle to ...
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### polynomial approximation around the point

I'm trying to figure out how to approximate a function by polynomial around the point. I'm aware of Newton's series and it is almost what I need, but it uses either forward or backward differences, ...
1answer
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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 ...
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### Romberg's algorithm for integration

what does the row and the column in Romberg's algorithm for integration indicate? I assume that the column represents the integration value with smaller intervals considered for calculating the ...
1answer
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### How to find a formula relating three values?

I haven't studied maths since high-school (20 years ago) and would like to find a formula to relate these values: ...
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### How to extrapolate daily values from a set of 30-day stats

I use a system (Slack) which provides analytics on user activity - namely, messages sent within a time window of the last 30 days. These 30-day totals are recalculated every 24h. I have these daily-...
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### Extrapolation of points by a function

I have got a positive series convergent series $w_j$, which is convergent. I can calculate a finite amount of terms $\sum_{j=0}^{j^*}w_j$ and would be interested in the estimation of the sum of the ...
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### Please explain how Richardson Extrapolation is used in this example

I am having a hard time understanding what on earth Richardson Extrapolation is trying to do. Consider the example of approximating $\pi$ by inscribing regular polygons in a unit circle. The ...
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### Norm of laplacian in dual space $H^{-2}$

how we can prove the estimate $\|\Delta u\|_{H^{-2}} \leq C \|u\|_{L^2(\Omega)}$, where $\Omega$ is a bounded open set of $\mathbb{R}^n$, and $H^{-2}$ is the dual space of $H^{2}\cap H_0^1$. Can we ...
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### How to find more accurate numerical integration result using Richardson's Extrapolation given midpoint and trapezoidal conditions?

This question has been confusing me. Any help would be very appreciated.
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### Most accurate finite difference result for first derivative [closed]

I got a problem in my assignment: obtain the most accurate finite difference results possible for the first derivative of f (x) = exp(cos(x)) at x=1, h = 0.5, 0.25, 0.125,...2^{16}. I have to do this ...
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### Taylor series and extrapolation 2

Hey guys, I've finished the first three parts, but I have no idea how to approach part d and part e. Any hints would help! Thanks! Update: I've finished the first three parts. For part d, I found the ...
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### Extrapolation and Splines

If you have a smooth curve, and at a certain point in time you want to predict the next turning point, and you assume it is a non-periodic, stationary, smooth process, then what would be the best way ...