# Tagged Questions

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

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### 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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### 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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### 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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### 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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### 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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### 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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### What is the Chebyshev method for InterpolationFunction?

With InterpolationOrder -> All, some methods of NDSolve returns interpolations with ...
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### 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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### 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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### 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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### 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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### 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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### Update NumericalFunction in NDSolve

I have NDSolve StateData from an NDSolve ...
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### 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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### Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
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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### 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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### 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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### 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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### 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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### 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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### Taking the derivative of the complex conjugate/absolute value of an interpolating function

I have following code: ...
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### 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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### 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 ...