Tagged Questions

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

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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 ...
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55 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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53 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
27 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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37 views

How to calculate a variable from another

There are two parts to this mathematics problem. Part A: Variables a and b I have the following facts: When a = 60, b = 21; and when a = 500, b = 163; How can I get the equation that will ...
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Extrapolating from an existing chart of numbers…

I have a chart that tells me that 1 Gallon of a material, say epoxy, will cover the following areas to their related depth: 12.5 sqft to 1/8" thick; 6.25 sqft to 1/4" thick, and; 3.0 sqft to 1/2" ...
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29 views

How to use Richardson extrapolation

In comment section in the question "Convergence of $\sum\limits_{k=1}^{\infty} \frac{1}{p_{k^2}}$, where $p_k$ is the $k$th prime" it is suggested that one first calculate $$ f(n) = \sum_{k=1}^{n} ...
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28 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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34 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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3answers
45 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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75 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
115 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
38 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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25 views

What method should I use for this optimization / feature selection project

I'm going to describe a problem and I'm not sure how to best solve it. I will describe the situation. When answering please recommend a method and maybe a software library. I'm using Python for my ...
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1answer
378 views

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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Well-behaved interpolation

I have a set of time-dependent scalar data. I would like to remove certain time intervals and fit the remaining data "well-behaved", which I cannot quite exactly define. The intervals may also be at ...
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1answer
22 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
169 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
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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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131 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
48 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 ...
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1answer
143 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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84 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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52 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
699 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
63 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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1answer
1k 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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142 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: ...
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308 views

Simpson's Rule derived from Trapezoidal Rule

I was just wondering if I could have some assistance in regards to the Trapezoidal Rule and Simpson's Rule. I have a question where it asks to generalize the Trapezoidal Rule to the case of ...
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1answer
153 views

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 ?
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784 views

Exponential extrapolation

Given a set of points on 2D surface $(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)$ and a function $f(x)=k+ab^x$, the task is to find values of $k,a$ and $b$ that minimize the following sum: $$\sum_{i=1}^n ...
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217 views

Next Point in a Curve?

If I have a series of data points that can be plotted as a curve, but I don't know the underlying function responsible for this, how can I calculate the next data point in the curve? The data points ...
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1answer
178 views

Construct an extrapolation table with optimal rate of convergence for cubic spline approximation

Let $S$ be a cubic spline interpolant that approximates a function $f$ on the given nodes $x_{0},x_{1},...,x_{n}$ with the boundary conditions: $S''(x_{0})=0$ and $S'(x_{n})=f'(x_{n})$. Use $S$ ...
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221 views

Kalman filter and data extrapolation

Context of the situation: I have a system set up that can give me the position of a person in a room. I also have a light that shines on this position. However, the light are lagging behind by 0.300 ...
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91 views

How to model a system for tracking a person using kalman filter?

I need to model a system for human motion. The following link shows for to build a system for a plane. I am currently reading the documentation for a kalman filter library ...
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365 views

Extrapolating to derive an $O(h^3)$ formula

The Forward difference formula can be expressed as: $$f'(x_0)={1 \over h}[f(x_0+h)-f(x_0)]-{h\over 2}f''(x_0)-{h^2 \over 6}f'''(x_0)+O(h^3)$$ Use Extrapolation to derive an an $O(h^3)$ formula for ...
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445 views

Extrapolate from these non linear numbers [closed]

How do I extrapolate from these non linear values? https://docs.google.com/spreadsheet/ccc?key=0AihZQktdW9mxdEdqNGJaOEtBOENVQXdfa1ZOWUhIamc I'm looking for a formula that'll give me more values down ...
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210 views

How to find $P(n+1)$, given $P(x)$ for $x = 0,1,\ldots,n$?

Given $P$, a polynomial of degree $n$, such that its values at $n+1$ points are $P(x) = r^x$ for $x = 0,1, \ldots, n$ and some real number $r$, I need to calculate $P(n+1)$? Can this be done without ...
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475 views

Solve for the intersection point, given two sets of data

I need to (numerically, specifically in C++) solve for the intersection point of two curves, f(x) and g(x). I am given two sets of data, one for each curve (eg. ...
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62 views

What general function or rounding method can be derived from these number series?

OK, first of all, don't laugh, this is related to a social iOS game, but I promise there is some real juicy math here... I am attempting to derive a general formula or algorithm that can predict the ...
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2answers
141 views

Deriving the formula and its error

$$f''(x) \thickapprox\dfrac{1}{2h^2}[f(x+2h) - 2f(x) + f(x - 2h)]$$ I'm supposed to be deriving the above formula and establish an error formula in using them. This is one of a series of problems ...
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263 views

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 ...
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149 views

Extrapolation of an analytical function

Given a function $f:z\mapsto f(z)$ for a discrete set of points in the real interval $z\in[a,b]$ and the knowledge that $f$ is analytical along the real axis and that its Fourier transform is real ...