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

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284 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 ...
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678 views

Interpolate throughout a 3d data list without extrapolation

I have a 3D list of data for which I'd like to plot an interpolated surface. There are several ways to achieve this, but none I cannot find a method which ONLY plots the ENTIRE interpolated surface ...
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56 views

InterpolationOrder has no effect on ListContourPlot when the data is of the form {x,y,f[x,y]}

This is related to the issue brought up here, if you want to mark it as duplicate feel free to do so, but it is slightly separate. Take two sets of data, identical except for the form, ...
4
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445 views

Cubic polynomial interpolation with velocities listed rather than some points

I am trying to use the function BSplineFunction[] to create a natural cubic spline. Normally what is done is that you specify "SplineDegree -> 3" and include a list of points and it will carry out ...
3
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0answers
44 views

Weird behaviour for a vector InterpolatingFunction inside an NDSolve

I have run into some weird behaviour on the part of NDSolve which I find pretty bizarre and which I would like to understand better. Suppose, for the sake of ...
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0answers
68 views

Data Interpolation of deaths by date

I am working with an ebola dataset from Guinea, 2014:(http://currents.plos.org/outbreaks/article/estimating-the-reproduction-number-of-zaire-ebolavirus-ebov-during-the-2014-outbreak-in-west-africa/). ...
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0answers
51 views

Problem with MissingDataMethod

Given v = {2, 1, Missing[], 5, 7, 4}; I use EventSeries to replace the missing value with its predecessor ...
3
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89 views

Data smoothing in three dimensions

I have data with statistical fluctuations of the form $f(x_i,y_i)$ over a discrete grid. I now need the values of $f(x,y)$ also at points other than the grid points. That can be achieved by ...
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66 views

Diagonalisation of equations for NDSolve

I have a linear matrix differential equation and I wish to speed up evaluation by diagonalising using eigenvectors. There is an example in Help for finite elements under "swinging beam" that is ...
3
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87 views

Defining a region from combination of data and geometric region

I would like to define a region in (x,y) by combining the region RegionPlot[ ImplicitRegion[ Sqrt[x^2 + y^2] <= 0.99, {{x, 0.01, 0.99}, {y, 0.01, 0.99}}]] ...
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88 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): ...
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454 views

How to make 3D object smooth?

This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica. I want to get smoother ...
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78 views

Construct single InterpolatingFunction from a mathematical combination of other IF's

Let's say I have an interpolated function f, like I might get as the solution to an NDSolve: ...
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0answers
56 views

Update NumericalFunction in NDSolve

I have NDSolve` StateData from an NDSolve` ...
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0answers
111 views

Interpolation of Singular Functions

I am trying to interpolate discontinuous functions for R in interval $[0,100]$ and r in interval $[0,100]$: ...
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0answers
234 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
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0answers
45 views

How to fix the error InterpolatingPolynomial::ipdup: The abscissas are not distinct

I'm trying to plot the function Abs[InterpolatingPolynomial[..] - f[x]] where f is a function. I receive the error: InterpolatingPolynomial::ipdup: The ...
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0answers
34 views

Find interpolation polynomial using newtons formula

I found this program for calculating the interpolation polynomial using Newtons formula. This function takes as input data points and returns a polynomial. For example: I want to find the ...
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0answers
84 views

Determining the order of continuity (smoothness) of a function

Is there any method to determine the order of continuity of a function (just like an interpolant) over a given domain, or at least determine the continuity on a given order? For example, according to ...
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0answers
54 views

Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...
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52 views

Using Quantity[] units causes errors in my calculation

I have an interpolation function in which I wish to use actual units. If I perform the calculation normally, it works fine and returns a proper FittedModel. To illustrate my problem, consider the ...
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58 views

Improving RationalInterpolation Result

The following code produces a {4,4} rational interpolation approximation accurate to 10^-6 or better over the range ...
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56 views

Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
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430 views

Change of coordinates for an InterpolatingFunction

This is a toy example of the question I have but I think it illustrates the point. I have a function y[x] which is an interpolating function. Let's define it ...
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433 views

Interpolating function as a model in Mathematica's procedures for fitting

Is it possible to use interpolating function with parameters as a model for NonLinearModelFit (and other integrated methods for fitting)? Similar question was ...
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46 views

Interpolation of 4D data on a triangular grid

I need to interpolate a function defined on a triangular surface (grid). The grid is defined as ...
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85 views

Find the (gaussian) function to fit a series of points?

I have a series of measurements for concentration of pollutant on a river C(x,t) where x is the location on the river and t is the timestamp. When plotted these data suggests a bell curve like Gauss ...
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90 views

Absurd solution by LinearSolve

I am trying to find curve that passes through all the data points.To do this i am doing interpolation using LinearSolve. No. of equations vary from 1000 to 3000. LinearSolve gives me values of ...
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56 views

NIntegrate on Interpolated function has evaluated to non-numerical value

I want to define a function that interpolates and integrates input data. Because I want to use Findminimum on the function I need to tell Mathematica, the function is only to be evaluated at Real ...
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183 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: ...
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352 views

Interpolation of multidimensional data organized logarithmically

The following threads call our attention to the fact that "accuracy of Interpolation will be worse with an unstructured grid", in the context of interpolation of 3d data: interpolation of 3D data ...