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

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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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26 views

Richardson extrapolation for set of points

I have a boundary element method code which gives me the numerical solution of a problem. The finer mesh I use, the more exact will be the answer. So I have a set of points as my answers. I want to ...
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1answer
72 views

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 ...
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1answer
20 views

Finding a curve given only its basic form and its tangent line

The basic form is $f(x)=k\sqrt{x}$ and the tangent line is $4x+36$. I've spent over half and hour with wolfram alpha and my notes on this problem: I've tried $(k\sqrt{x})'=4x+36$ and got ...
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1answer
53 views

Estimating landing position for a slowly falling object using latitude, longitude, and altitude.

I have a weather balloon project, in which I intend to use GPS to locate the payload when it finally comes down again. I will make the computer send coordinates to a server every minute or so, as ...
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2answers
95 views

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 ...
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26 views

Estimate the error of interpolation/extrapolation

I'd like to know how we can estimate the error of interpolation. For example, let's consider Lagrange interpolation. We don't know anything about the real function (it could be an algebraic or a ...
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1answer
9 views

Estimating the value of a variable based on the existing variable?

Need your help with a math problem I having trouble to solve. Let's say when we buy an item we need to pay 100 and the tax would 10 percent. So my buying cost becomes 110. And when I go to sell it ...
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1answer
22 views

Extrapolate data points from a series of averages

Given a series of data points: $$\begin{array}{c|c|c|c|c|c|c|c|} & \text{Monday} & \text{Tuesday} & \text{Wednesday} & \text{Thursday} & \text{Friday} & \text{Saturday} ...
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1answer
84 views

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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1answer
47 views

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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27 views

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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1answer
92 views

Chebyshev Interpolation

I'm studying Chebyshev Interpolation at the moment. Here n points $$x_1, x_2,..., x_n$$ are chosen within the interval $$-1 \le x \le 1$$ Using the Lagrange formula and minimising, we get: ...
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1answer
76 views

How to extrapolate with these values

I'm reading a paper by Yallop and in it he gives the following table of values: $$\begin{array}{|c|c|c|c|c|c|c|}\hline x &0.3 &0.5 &0.7 &1 &2 &3\\ \hline y ...
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0answers
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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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41 views

How should i apply Richardson Extrapolation?

I trying to understand how the Richardson Extrapolation works, and what it is good for. The internet has lots articles about the this, but they all seem to lack in what it is useful for. I wanted ...
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1answer
107 views

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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32 views

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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33 views

Extrapolation: Richardson , Taylor

Does a first order approximation only use $f(x)$ and $f’(x) $ with $f’’(\theta)$ in the error? While second order would include$ f’’(x)$?
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$(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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2answers
268 views

Bezier extrapolation

The red dots are my data: I know that they are on a Bézier 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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1answer
109 views

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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23 views

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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66 views

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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1answer
75 views

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 ...
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119 views

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 ...
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1answer
314 views

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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1answer
71 views

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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1answer
266 views

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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1answer
51 views

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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270 views

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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201 views

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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2answers
109 views

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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1answer
839 views

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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1answer
52 views

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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1answer
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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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1answer
51 views

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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1answer
1k views

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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1answer
177 views

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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2answers
750 views

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 ...
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1answer
112 views

Extrapolate lat/long to x.y

I'm trying to convert lat/lon coordinates into x,y coordinates onto an image of a fixed size (800x600) I know the maximum lat/long and the minimum lat/long and I know the image size, is it possible ...
2
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1answer
227 views

Help in this exercise about Richardson extrapolation.

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 $10^{-2}.$ ...
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1answer
118 views

Numerical Analysis - Richardson Extrapolation

Question: Suppose that N(h) is an approximation to $M$ for every $h > 0$ and that $M = N(h) + K_1 h + K_2 h^2 + K_3 h^3 +\cdots$, for some constants $K_1, K_2, K_3,\cdots$. Use the values $N(h), N( ...
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75 views

Need an equation to fit this exponential curve

I need a curve that grows exponentially. Only 2 data points are important: (0, 0) (1, 1) After that, I just need to be able to play with how much the graph ...
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1answer
3k views

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 ...
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1answer
144 views

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.
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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 ...
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7k views

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 ...
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2answers
161 views

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: ...