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

learn more… | top users | synonyms

0
votes
1answer
27 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 ...
0
votes
0answers
7 views

Progress Estimation

I wrote some programs lately which grind through big sets of data and I would like to add to them some prediction on the remaining time needed to finish. Last time I tried this I used simple linear ...
1
vote
1answer
23 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 ...
1
vote
1answer
44 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: ...
0
votes
1answer
40 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 ...
3
votes
0answers
43 views

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 ...
0
votes
0answers
19 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 ...
1
vote
1answer
41 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 ...
0
votes
0answers
14 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; ...
0
votes
0answers
31 views

Could you please explain the algorithm for the below given number series generated by Excel Fill series?

Below images represent the number series that are obtained using the Excel Fill Series If you input 13, 16, 17 then 19.33333, 21.33333, 23.33333, 25.33333,.. is generated. If you input 34, 424, ...
0
votes
0answers
24 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)$?
1
vote
0answers
20 views

$(x,y)$ 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 ...
1
vote
2answers
170 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 ...
2
votes
0answers
20 views

How to calculate this integral (with limit afterwards)?

I have to calculate this integral with limit: $$ G(m,n; E) = \lim_{\epsilon \rightarrow 0^+} \iint_{-\pi}^{+\pi} d k_x d k_y \frac{e^{i(k_x m + k_y n)}}{E+ i \epsilon + 2\cos k_x + 2\cos k_y } . $$ ...
1
vote
1answer
74 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 ...
1
vote
0answers
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 ...
1
vote
1answer
64 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 ...
0
votes
1answer
53 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 ...
2
votes
0answers
72 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 ...
1
vote
1answer
190 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 ...
1
vote
1answer
66 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 ...
2
votes
1answer
144 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 ...
0
votes
0answers
40 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} ...
2
votes
1answer
41 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?
0
votes
0answers
134 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 ...
0
votes
3answers
111 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 ...
0
votes
2answers
99 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) ...
1
vote
1answer
453 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 ...
0
votes
1answer
43 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 ...
1
vote
1answer
865 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 ...
0
votes
1answer
35 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 ...
1
vote
1answer
610 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 ...
2
votes
1answer
135 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 ...
0
votes
2answers
430 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 ...
0
votes
1answer
78 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
votes
1answer
186 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 $10^{-2}.$ ...
1
vote
1answer
103 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( ...
0
votes
2answers
64 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 ...
3
votes
1answer
2k 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 ...
1
vote
1answer
83 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.
3
votes
0answers
47 views

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 ...
1
vote
2answers
3k 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 ...
3
votes
2answers
148 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: ...
1
vote
0answers
406 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 ...
0
votes
1answer
211 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 ?
1
vote
3answers
1k 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 ...
1
vote
2answers
366 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 ...
1
vote
1answer
202 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 $S$ ...
1
vote
1answer
312 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 ...
1
vote
1answer
110 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 ...