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

learn more… | top users | synonyms

0
votes
1answer
22 views

Calculate the partial vapor pressures of a variable at xB = 0.75 based on the interpolation functions of the data

I'm having troubles in solving an exercise for an assignment in my Chemistry course. Talking about interpolations, I've already have a graph but I need to:(c) Calculate the partial vapor pressures of ...
6
votes
1answer
144 views

Interpolation on a regular square grid spanning a triangular domain

Context I am trying to identify contours of a function which is sampled on a cartesian grid within an irregular (triangular) region. Here is the data ...
18
votes
3answers
1k views

Monotone, periodic 1d-interpolation with continuous 1st order derivative

Lately, we had this thread about interpolation where J. M. linked two interpolation methods. The background for my question is that I estimated a parameter in polar coordinates with dependence on the ...
2
votes
1answer
41 views

Interpolate a discrete vector field

I have a discrete vector field, from which I want to derive the continuous one. For example, the planar vector field is defined by: ...
0
votes
1answer
51 views

Using InterpolatingFunction in equations

I tried to use InterpolatingFunction in another ODE, but it doesn't work, because it seems for Mathematica that 2 functions are unknown instead of one. ...
17
votes
4answers
1k views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
0
votes
1answer
56 views

Interpolating a non-continuous set of points

I'm trying to create a pure function that I can feed into OutputResponse[ ] as the input u[t]. In order to do this, I've written code to create a square wave pulse train in the form of a collection of ...
1
vote
1answer
48 views

how to reduce noise in time series data?how to do interpolation for missing value data?

i have done this coding to plot the data. the problem is some value is missing for certain date and the graph is not smooth and noisy. one way to smooth the data is by interpolation but i dont know ...
3
votes
2answers
81 views

Numerical root-finding: Find leftmost root in a domain

This is surely a duplicate, but I cannot seem to find a similar question. I use NDSolve to find an InterpolatingFunction y[t] ...
1
vote
1answer
136 views

Line integrals over a path defined by a set of points (rather than an analytic formula)

I'm getting inaccurate results when computing (plotting) the value of a function against the length of a line integral, where the path comes from a set of numerically calculated points. (In contrast, ...
2
votes
3answers
196 views

Function to calculate average of multiple lists

I have several lists of experimental data f[x] with different intervals Δx including some noise. ...
0
votes
1answer
47 views

Numerical integration of a three dimensional array

I need to integrate a scalar valued function $f\left(\boldsymbol{x}\right)$ where $\boldsymbol{x}$ is a three dimensional position vector; in other words: $\int_{\Omega} f\left(\boldsymbol{x}\right) ...
2
votes
1answer
99 views

Find tangency of InterpolatingFunction and circle

I am trying to use a system of equations to solve for the common tangent of a (polar) InterpolatingFunction and a circle. Unfortunately, both NSolve and FindRoot don't yield results, even when I ...
6
votes
0answers
119 views

Interpolation on an unstructured (mostly-structured) grid in 4D+

I frequently need to perform interpolations on an unstructured grid. Mostly, with the purpose of filling grid holes and then later continue with regular grid interpolations. Mathematica V9 and V10 ...
0
votes
0answers
52 views

Interpolation of a NURBS curve

Known that NQ=P where N is the Bspline basis function, Q is the control point that we wish to locate, P is the data points given ( the curve must pass through it) is there any way to modify the "N" ...
1
vote
1answer
55 views

Making a movie from an interpolating function

Say I use some Mathematica procedures to find an interpolating function of two variables: $u(x,t)$. Is it possible to make a movie of this interpolating function, i.e. plot it on a certain line $x \in ...
3
votes
0answers
43 views

Strange extrapolation in ListContourPlot?

I have some Table of {x,y,z} values (energy as a function of radial and azimuthal frequencies in a galaxy if you care to know): ...
3
votes
2answers
63 views

FunctionInterpolation with vector output and scalar input

Apparently it is possible to build and InterpolatingFunction that accepts a vector input and returns a vector output: ...
1
vote
2answers
87 views
15
votes
4answers
4k views

Getting the interpolation function from a list plot

I have conducted a chemistry experiment and obtained a list of concentrations of a reactant against time. I plot a graph of this using Mathematica's ListPlot ...
2
votes
0answers
84 views

Position from 3 dimensional acceleration data? [closed]

Per a previous post on Mathematica StackExchange here I'm trying to utilize 3-axis accelerometer data to determine approximate 3D position. I wanted to start with a simple case. To this end I've ...
2
votes
2answers
102 views

Derivative of Vectoral NDSolve Interpolated Function / Rule Solutions,/., and Vector NDSolve [duplicate]

I need to find the instantaneous phase and instantaneous frequency for a rotating system. I am having difficulty making the math work with interpolating functions. First, here is a problem without ...
6
votes
2answers
259 views

ListContourPlot interpolation fails if x and y axes have different scales

To summarize what is below: ListContourPlot doesn't work when the domain has different x and y scales (fails when x/y~10^4, which seems surprisingly small). Is it possible to call ListContourPlot ...
0
votes
1answer
52 views

How to fit this data to be used in NIntegrate later?

I have a list of data points that resemble a chi-squared distribution (long tailed gaussian) that I am having trouble fitting or finding an equation with. The goal is to use the fitted equation in an ...
1
vote
0answers
124 views

NDSolve: Equation with interpolating function [closed]

I have a question regarding DSolve and NDSolve functions in Mathematica 10. For instance, I'd like to solve an ODE: ...
-3
votes
2answers
135 views

Aitken interpolation of a polynomial?

How I can approximate a polynomial using Aitken's scheme using two nodes for the interpolation? ...
3
votes
3answers
150 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
64 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
2k 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
123 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
104 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
82 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 ...
0
votes
0answers
38 views

Improving RationalInterpolation Result

The following code produces a {4,4} rational interpolation approximation accurate to 10^-6 or better over the range ...
7
votes
2answers
709 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
70 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
99 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
27 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
175 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
85 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
67 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
123 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
99 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
74 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
79 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
46 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
51 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
69 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 ...