Questions on the interpolation functions in Mathematica (Interpolation[], ListInterpolation[], FunctionInterpolation[], InterpolatingPolynomial[], etc.)

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-3
votes
2answers
141 views

Aitken interpolation of a polynomial?

How I can approximate a polynomial using Aitken's scheme using two nodes for the interpolation? ...
4
votes
3answers
179 views

Transform an InterpolatingFunction

I'd like to transform an InterpolatingFunction from NDSolve but can't figure out how. Here's an example. The equation I want to solve is ...
1
vote
1answer
70 views

Interpolating a polynomial for with first and second derivative of points

I am trying to fit a polynomial for switch cutoff which is used in Molecular dynamics. I want a fifth order polynomial with six coefficient $c_0, ...,c_6$ between $r_1<r<r_2$ with these ...
20
votes
6answers
3k views

Finding the intersection of a curve with an interpolation function

There are no issues trying to find the intersection points of two defined curves. ...
2
votes
1answer
142 views

Smooth animation of ListLinePlot

I have a sequence of 2D-points from uniformly sampling a time dependent process and plot this sequence with ListLinePlot. For example: ...
2
votes
1answer
115 views

How do I find out what a Mathematica function is doing (which numerical method it uses and how)?

Long story short, I am working on a project which entails fixing a bug I have found in Mathematica (8 and 10). In general, I would like to know what a specific Mathematica function is actually doing ...
-1
votes
1answer
85 views

Reduced interpolation order [closed]

I have a problem with Interpolation - the order is reduced to 1 no matter what, but I need a quadratic interpolation order. The ...
7
votes
2answers
745 views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...
1
vote
1answer
73 views

how to make interpolated data as a function?

For example, data1 = 0 1 1 2 3 3 5 2 6 2 9 4 11 5 13 6 14 7 16 8 data2 = 0 2 1 3 2 2 3 1 4 2 6 3 8 4 9 6 11 4 16 7 each data have different x-axis interval. so ...
3
votes
1answer
113 views

List interpolation

Hi mathematica people! So i am looking for the best way to interpolate a function given a list of its values. I have an iterative algorithm which needs high precision otherwise the numerical noise is ...
0
votes
0answers
28 views

Why numerical functions can't digest InterpolatingFunction with units?

Answering this question gave me the idea that I must be missing something.. In brief, numerical functions generally 'understand' units: ...
1
vote
3answers
204 views

Developing a function of two variables from given data

Cross listed from MSE: http://math.stackexchange.com/questions/1029399/developing-a-function-of-two-variables-from-given-data (I believe Mathematica SE is an appropriate place to ask this, as well.) ...
1
vote
1answer
109 views

What extrapolation method does Interpolation use by default? [closed]

As far as I can tell, Interpolation uses cubic spline interpolation by default - please correct me if I'm wrong. What does it use for extrapolation outside of the ...
0
votes
0answers
47 views

How does Mathematica interpolates? [duplicate]

In manual for Interpolate function it is said, that possible method of interpolation is Hermite. Unfortunately, I can't see ...
0
votes
0answers
96 views

plotting the stable and unstable manifolds of a difference equation

I have a 2D non-linear system of difference equations for variables x and y defined as follows: ...
3
votes
1answer
132 views

Interpolation function rejected by ParametricPlot3D

I was playing around with the bouncing ball example, and decided to make a 3d version. I decided to use ParametricPlot3D for a simple independent 3D ...
3
votes
1answer
108 views

How to evaluate differential entropy from raw data?

I want to evaluate the differential entropy according to here $$h(X) = - \int f(x) \log{f(x)} dx$$ where $f$ is the probability density function. Lets create some test data (normal distribution): ...
2
votes
1answer
95 views

BSpline or other curve through arbitrary ordered sequence of two-dimensional points

How does one create a BSplineCurve or other smooth curve passing through each point in an ordered list, where the curve may be non-simple, i.e., can double-back upon itself, loop, and so forth as for ...
1
vote
1answer
83 views

Series expansion of InterpolatingFunction obtained from NDSolve

I am trying to obtain a series expansion of the numerical solution of a differential equation. I encounter difficulties going beyond first-order expansions which I believe might be due to my inability ...
0
votes
0answers
53 views

Combination of interpolations doesn't work?

I have a table valued functions f[i_] and g[i_] and I need to plot various combinations of the function and its derivatives (for example: f''f, f'/f). I tried interpolating f[i_] to ->f[x] and ...
1
vote
0answers
60 views

Interpolation of Singular Functions

I am trying to interpolate discontinuous (1/R-r)EllipticK[r/(R-r)^2] functions for R in interval $[0,100]$ and ...
7
votes
3answers
4k views

Get polynomial interpolation formula

I'm attempting to get a polynomial interpolation formula out of Mathematica but I am absolutely lost. I stared out using ...
1
vote
1answer
72 views

NDSolve with a constant

I have a simple differential equation like this s = NDSolve[{y'[x] == A y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] where $A$ is a constant. Mathematica gives ...
6
votes
2answers
213 views

2D smoothing spline interpolation

Does Mathematica have 2D smoothing spline interpolation built in? I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would ...
12
votes
1answer
724 views

Curve fit based on minimal data

Inspired by the fantastic answers here and here, I would like to ask a questions along similar lines. I have 6 curve types that follow these rules: Type A: If point 1 is positive and point 2 is ...
5
votes
2answers
396 views

Suppress extrapolation of interpolating function in a ContourPlot

I have defined an interpolating function, myfcn[x], valid on the domain x = 0 to 1.5. I am then using ...
11
votes
2answers
219 views

Temporal database reconstruction in mathematica

<EDIT> after some internet research I found the database domain that deals with this kind of thing: Temporal Databases. I think my question therefore becomes how to reconstruct a temporal ...
3
votes
1answer
91 views

Fast list interpolation over common x,y for multiple variables

I have a (long, >50K elements) unstructured list with a header similar to; AList[[1]] = {x,y,z,var1,var2,var3,var4,...,varN} I want to interpolate z, var1, var2, ...
0
votes
2answers
107 views

Select pairs of columns from an array of data [closed]

I try to interpolate the first two columns of a seven-column file formatted as follows: ...
10
votes
5answers
485 views

Multidimensional interpolation with duplicate abscissa values [duplicate]

I am trying to do a first order interpolation on a multidimensional data set containing duplicate abscissa values (which Mathematica does not like), like this one: ...
1
vote
2answers
256 views

How to know form of plotted Bezier function

Simple scenario is to see the Bezier function, but how to know which polynomial approximate it? ...
1
vote
1answer
202 views

Can I use the values of interpolating points from NDSolve's output? And How?‎

The output of NDSolve is a (list of)InterpolatingFunction(s). In standard output format the ‎elements of interpolation are not ...
11
votes
1answer
202 views

Incompatible InterpolatingFunction between V9 (and earlier) and V10

Bug introduced in 10.0.0 and fixed in 10.0.1 I am encountering compatibility issues when loading DumpSave(d) definitions in V10 that have been created with ...
1
vote
0answers
58 views

Show actual Interpolation function [duplicate]

Is there a command to show the actual function when using the Interpolation command? For example, f = Interpolation[{1, 2, 3, 5, 8, 5}] returns ...
8
votes
2answers
308 views

Interpolating an Antiderivative

I'd like to be able to make InterpolatingFunctions for antiderivatives of functions that can't be integrated symbolically. However, the following code returns several error messages: ...
12
votes
2answers
435 views

Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
0
votes
2answers
105 views

Replace $z$ with interpolated function and plotting

I start off with this equation $z(x,y) = sin(xy)$. I create an interpolation from $0 < x < 5$ and $0 < y < 5$. I then use this interpolation on a simple function $w(x,y) = x + y + z(x,y)$ ...
1
vote
2answers
192 views

Integrating Squared of Interpolating Function with respect to one variable

I am interested in evaluating a two dimensional interpolating function produced by solving the wave equation. Here is the code that includes the resulting interpolating function. ...
2
votes
2answers
240 views

How do I feed data points into an equation to solve NUMERICALLY?

I start with this equation and solve it numerically for $z(x,y)$ in the range $1 < x < 5$ and $1 < y < 5$: $$ \frac{3}{xyz} - 2x - 3y - 5z = 0 $$ Then using the data points of $z$ above, ...
8
votes
2answers
252 views

interpolating function over dates

I've got a bunch of readings at various dates and times. I'd like to be able to interpolate and then integrate over, say days. I can do this by converting my date/time to ...
0
votes
0answers
68 views

Is there a reason why some specific arrangement of scattered grid points would yield bad RBF (Obtuse package) interpolation results?

I have an arrangement of grid points given by the figure below (the datagrid data is posted below at the end of the post): They correspond to electrode positions of an EEG signal. I am ...
19
votes
2answers
500 views

Object separation from a 2.5D surface

I'm trying to identify the shape and the boundaries of objects. The data was generated with a laser scanner and represent the surface of an area in which many boulders lay on the ground and making up ...
0
votes
1answer
187 views

Interpolation of 4D data

To create a table and an interpolation function of 3D data T=f(X,Y) I have the answer here: interpolation of 3D data How to create a table/interpolation function of 4D data T=f(X,Y,R)? If I do ...
3
votes
1answer
222 views

Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse?

I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ...
6
votes
2answers
260 views

Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug?

More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ...
1
vote
3answers
120 views

Removing some data and replacing them with new ones

I have a data list where the elements have the form (time, velocity ). I need to remove some malformed elements in places where the data does not change smoothly and then replace those points by ...
1
vote
1answer
47 views

Interpolation function evaluation and timing

Lets define two identical functions $f$ and $g$ in a slightly different way ...
0
votes
1answer
162 views

Better code for two variable fractal interpolation functions

I am trying to write code for 2-variable fractal interpolation functions using two iterated function systems and two starting functions (both $y(x)=x$) which creates a sequence of piecewise defined ...
5
votes
3answers
536 views

Piecewise Polynomial Interpolation

Given some data pairs $(x_i,y_i)$, with $i=0,...,m$, and a degree $r$, I wish to build a piecewise polynomial function to interpolate these data. That interpolation should be continuous, and, on every ...