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

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347 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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76 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, ...
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754 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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65 views

N[Integrate] failing to return an accurate result from an interpolated integrand

I need to N[Integrate] a function Cos[alpha*x]*f(x) between x=0 and 30 at increasing alpha-values. Here f(x) is an interpolated function derived from a set of 120 ...
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43 views

Multi-variable FunctionInterpolation with the range of one variable as a function of another

How can I modify my FunctionInterpolation code so that the boundary of one of the variables is a function of another variable? ...
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472 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 ...
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42 views

What is the Chebyshev method for `InterpolationFunction`?

With InterpolationOrder -> All, some methods of NDSolve returns interpolations with ...
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59 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 ...
3
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75 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/). ...
3
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80 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 ...
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490 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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136 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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66 views

Update NumericalFunction in NDSolve

I have NDSolve` StateData from an NDSolve` ...
2
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0answers
138 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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301 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
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62 views

Smoothing ListContourPlot contours for unstructured grids. Part 2

My question is motivated by the following discussion. Smoothing ListContourPlot contours I need to generate high-quality contour plots for some property generated on a non-rectangular grid. This is ...
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64 views

Obtaining values from interpolating functions

A similar question has been asked in the post HERE but the current question is more complicated: I have the following differential system ...
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62 views

How to use interpolating functions in NSolve with a piecewise function?

I have a system of two non-linear differential equations that are piecewise, the solutions of which I would like to use to obtain the values of a third variable that is also piecewise. I have trouble ...
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47 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
90 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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60 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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56 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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70 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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60 views

Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
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486 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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494 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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Interpolating functions and NDSolve

I've been working on trying to get Mathematica to solve this system for a while now, and I have a couple of questions relating to various parts of the system: Interpolating functions: As a number of ...
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22 views

3DPlot, Logarithmic x and y axes, Interpolating function

I've used NDSolve to get an InterpolatingFunction that solves a certain difeq. I want to see the behavior of this function on a couple different scales, so I want to use some sort of Log Plot. For a ...
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63 views

How to plot an interpolating function from data showing the median values and the scatter around the medians

I have a list of data points $x_{i}$, $y_{i,16}$, $y_{i,50}$, and $y_{i,84}$ where $y_{i}$ respectively correspond to $16th$, $50th$ and $84th$ percentiles value of the function at positions $x_{i}$. ...
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46 views

Check if interpolated function passes through a specified region

Is there an efficient way to check if a curve that was obtained as an Interpolating Function (from solving differential equations numerically) passes through a given region? I am solving for two ...
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40 views

NSolve with a term that is an interpolating function

I need to solve this system of equations Log[np[x]] + psi[x] + f[np[x], nm[x]] == 0 Log[nm[x]] - psi[x] + f[np[x], nm[x]] == 0 For ...
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93 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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97 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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244 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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400 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 ...