# Tagged Questions

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

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### Name of the field of study that details extrapolation of a series based on subset sample data

Apologies if my notation and/or terminology is way off - I'm not well versed in mathematics. I'm looking for the name of the field of mathematics that might help me solve my problem. Here's my problem:...
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### Romberg, trapezoidal rule exact for polynomials

My question is, how can I proof that the rombergs method of the summed trapezoidal rule is exact for polynomials with degree $(2n+1)$ or less. Thanks for helping, one or two tips can help me here. ...
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### Extrapolation of $c^{-3/2}$. Optimal data points?

I have a computer code that does some complicated calculations and results in a real number. At the end I had to perform a infinite sum, $$S=\sum_i^\infty x_i \;,$$ which I approximate by a finite ...
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### Extrapolating the sequence of derivatives of an analytic function

Suppose that $f(x)$ is an analytic complex or real function on the real domain and we only know $f(x_0)$ and the first $n$ derivatives of $f(x)$ at $x=x_0$. Is there an algorithm whose accuracy ...
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### What is the simplest way to estimate future values of two variables?

I have two variables such as x and y. The data is not increasing linearly. Also, I have restricted boundry [10;20]; x y 10 15 11 15,5 12 17 13 19 14 19,5 15 20 16 20,2 17 20,8 18 ...
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### Box-Jenkins and related extrapolation methods

I have been reading ARMA MODELS AND THE BOX JENKINS METHODOLOGY by S. MAKRIDAKIS AND M. HISON 95/45/TM . I seem to be just a little stuck on the idea of using "trends". I think of a "trend" as a $y$ ...
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### Find formula with Richardson Extrapolation based on centered difference formula

I'm preparing for my exams next week, and I'm making exercises as a preparation. Now, I'm asked to derive the following formula using Richardson Extrapolation based on the centered difference formula: ...
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### Richardson extrapolation: how to derive an approximation for $f'(x)$ with Euler backward/forward methods

We are told that the starting point is the difference $f(x+h) - f(x-h)$ (each of which represents it's own series; the last an alternating series) for getting the Richardson extrapolation. When I ...
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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 ...
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### Error in ratio approximation

Not being very familiar with statistics I have been trying to figure this out for some time: Suppose that I am trying to determine the relative amounts of several animal species. To do this, I find ...
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### Fine the value of $P(n+1)$ given values of $P$ from 1 to $n$ [duplicate]

$P(x)$ 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 ...
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### Best percentage change for trend

Consider the revenue of a company for the last five year and you want to to know whether there is an upward, downward or no trend. How would you calculate the "optimal" percentage change? I have an ...
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### What is the best way to extrapolate values for a 2 dimensional function?

I have a computer program that performs a task in a set of files. The time the program takes to finish is a function of how many files it is processing and the sum of their sizes, for example; ...
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### $(x,y)$ points extrapolation

My process is generating $x,y$ points. The points are result of tracking movement of an object so its a bit inertial. The tracked object can't change direction rapidly. I need to extrapolate data ...
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### Bezier extrapolation

The red dots are my data: I know that they are on a BÃ©zier curve of order 5 (6 control points). There are extra restrictions on the 6 control points A,B,C,D,E & F: A & B are on a ...
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### How to calculate this integral (with limit afterwards)?

I have to calculate this integral with limit: $$G(m,n; E) = \lim_{\epsilon \rightarrow 0^+} \iint_{-\pi}^{+\pi} d k_x d k_y \frac{e^{i(k_x m + k_y n)}}{E+ i \epsilon + 2\cos k_x + 2\cos k_y } .$$ ...
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### General name for interpolation and extrapolation

I would like to know if there is a technical term to cover both interpolation and extrapolation. The reason why I am asking is that I am writing a computer program to do interpolation and ...
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### Fitting curves by extrapolating known behaviours in certain limits?

I have been studying how a the rotation and translation of a sliding disc (think of it as a hockey puck) is affected by uniform friction. I encountered an integral that I was not able to solve, and ...
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### Pattern on polynomials disguising as exponentials

Recently I've been looking at integer sequences that look like exponential at the first few terms but is actual polynomial, like these two sequences [1] [2]. And there seems to be something ...
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### How to linearly extrapolate a quantity correctly?

This is a real world scenario of me trying to apply math and trying to find how much approximately I will be paid this month. Let's say I'm working 30 days a month. In the first 9 days of the month I'...
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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,...
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### Richardson Extrapolation - problems understanding how it works

I'm doing homework, and I am stumped on the first problem. I'm given this: Apply the extrapolation process described in Example 1 to determine $N_3(h)$, an approximation to $f(x_0)$, for the ...
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### Math C question related to diseases. [closed]

There are only 4 people in my math C class, including my teacher. We were given the question below and asked to find the answer, unfortunately we all have different answers. What is the answer to the ...
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### Implementation of Richardson extrapolation in mesh independence study

I am busy with a mesh independence study in computational fluid dynamics, where I am systematically refining my mesh and monitoring a certain parameter of interest with the goal that the value should ...
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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?
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### extrapolate boundary data of a 2d function

I have a function defined over a 2d domain. I want to keep all the internal data, but the information near the boundaries are less accurate and I want to extrapolate them from the inner points. Is ...
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### How to I extrapolate probability over a time period?

The probability of a "success" is 16% in 5 years. What is the probability of success in 10 years? How much time do I need for the probability to reach 70%? Is there a way to answer these questions ...
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### Compound interest with a compounding interest rate

I have an investment which pays 3% interest (r) annually but it also increases the interest rate every year by 5% (g). I re-invest all interest payments at the start of each year. How many years (t) ...
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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 ...
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### Why is extrapolation called extrapolation?

In interpolation we find a polynomial that passes through the points $x_0<x_1<\cdots<x_n$ and estimates $x\in[x_0,x_n]$, so we say the interpolation polynomial interpolates the points. But as ...
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### Richardson Extrapolation Matlab Code: Example and try out code included.

currently I am studying Numerical Methods in Matlab and I need a Matlab code which would calculate Richardson Extrapolation using data given in a table, respectively for x and f(x). For example: Use ...
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### Extrapolating values from a set of values in time

This is a question at the crossroads of mathematics and programming. I have a sequence of values that are generated every $300$ms. (Not exactly, but I know the exact time point of each value). I am ...
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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 ...
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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 ...
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### Extrapolation with exponential curve

I would like to extrapolate time series using exponential curve while getting the parameters via linear regression. Exponential curve is given as $g=e^{~a + b \cdot t}$. Since I want to use linear ...
We know $F(h)=a_0 +a_1h + a_2 h^3$ $F(1)=4$; $F(1/2)=21/8$; $F(1/4)=145/64$ Find a approximation of $F(0)=a_0$ with Richardson extrapolation method with an absolute error less than $10^{-2}.$ ...