# Questions tagged [interpolation]

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

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### How to find interpolated values in a list?

Consider a list as list = {1, 2, 3, 5, 8, 5}; If I apply interpolation on it, f = ListInterpolation[{1, 2, 3, 5, 8, 5}]; ...
1k views

### How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
2k views

### Ηow to create an interpolated CDF from its samples?

I want to use a distribution I have only aggregate statistics on, namely its CDF sampled at certain points. I would like to keep it "nonparametric" (remain noncommittal on the parametric form), but I ...
2k views

### Extracting polynomials from a cubic spline function

I have this set of three data points and I want the natural cubic spline functions for them: dat = {{-.0247500, .5}, {.3349375, -.25}, {1.101000, 0}}; I tried: ...
185 views

### Create a surface function from several plots

I'm quite new to Mathematica. I've used Matlab in the past but it was a long time ago. I'm working on developing a Dark Room Light meter and need to fit some curves. But, ideally, I need to fit all ...
138 views

### Derivative of Interpolation parameters

I am working with interpolation function with some non-numerical arguments. A simplified version of the function I am working with is: ...
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### How to interpolate my list of results?

I have the results ...
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### How to interpolate my results at discrete steps? [closed]

I have the results ...
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### How do I transform my results? List-manipulation? Interpolation?

I have the data ...
188 views

### Reducing a FEM 3D Interpolation Function to a 2D Interpolation Function

I'm trying to solve the heat equation in 3D using FEM and back out a slice in the xz plane. My problem is when I define a function that is a slice in the xz plane it uses the full 3D interpolation ...
189 views

### Plotting a 3D FEA solution on the mesh

I have obtained solution to a 3D FEA problem and would like to plot it on the mesh. The geometry has holes in it. For example, if u[x,y,z] is an interpolation function, obtained from a FEA solution, ...
324 views

### Building a 2D function by combining 1D functions

I have six 1D continuous functions that I want to use in order to find a 2D function. Each of these 1D functions has to be placed at a unique angle $\phi$ w.r.t the $x$-axis as given in the image ...
431 views

### Interpolation function and numerical integration

I've noted that the numerical integration time of an interpolated function depends on the size of its domain. If I create two lists from the same function with the same step size, but one having a ...
717 views

### Replacing variable in an equation with an Interpolating function polynomial and plotting residual

I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things. I imported the data and created an Interpolation polynomial with ...
605 views

### Custom interpolation on unstructured grid (2D, 3D)

as I'm not satisfied with the way Mathematica interpolates data on unstructured grids, I would like to implement my own interpolation. I will aim for Crouzeix - Raviart type of (quadratic) triangular ...
148 views

### Interpolation is not smooth

Consider a function ...
2k views

### Higher order periodic interpolation (curve fitting)

I have a list of points in 3D, and I want to get a smooth interpolation or curve fit (it is more for illustration) of these points such that the first and second derivatives at the start and end ...
384 views

### Finding self-intersections of a closed curve represented by an interpolation function

I've been trying to find particular simple closed curves on a plane. ...
32 views

### NMaxValue with complex interpolation

I've encountered a very strange problem. I'm trying to find a minimum of a real part (or absolute value, or really any possible real-valued expression) of some complex function, which was previously ...
140 views

### Add interpolating functions over an unstructured mesh to get a single interpolating function

In a Newton iterative FEM PDE solver I am writing, each iterative step involves updating the current solution function u by adding to it the increment function <...
53 views

### make time function with Interpolation of discrete time data and use this function in Solve and Plot

I have value of a and b in terms of time for discrete value of time. How can i make a time function with interpolation? after that and generate a[t_]:=Interpolation of some point in terms of time... ...
77 views

### Interpolation function precision in multi dimentional case

I have this interpolation example ...
187 views

### Interpolating the Treasury yield curve

The following code: scrapes current U.S. Treasury yield data from the Treasury's website; plots the available data points (from the 1, 2, 3, 5, 7, 10, 20, and 30 year instruments); and interpolates &...
226 views

### Unable to Solve Area Using Paramteric Equations derived from The Numeric Soution of a Differential Equation

I'm creating a test that measures the distribution of closed shape $\mathcal{C}$. This requires taking the average ray length (from $(u,v)$ in $\mathcal{C}$ to the boundary) using ray length per ...
161 views

### 3D interpolation to 'm x n' matrix

Let's consider an example: Case 1: ...
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### How can I speed up my compiled RBF interpolating function?

Overview I have a function that acts like the Interpolation on sparse $n$-dimensional data using a simple implementation of RBF interpolation method. I want my ...
60 views

### Interpolation with symbolic variable to speed up numerical integral [closed]

I have the following integral: $$E(r) = \int^{\infty}_0 e^{-x^2} e^{i\pi(ax^2 - \frac{x}{\Delta})}J_0(r\,x)x \,\mathrm{d}x,$$ where $J_0$ is the zeroth Bessel function of the first kind. Two ...
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### Finding intersections of two parametric curves

I am dealing with the root finding of two parametric data curves (data below). I have already checked Parametric Interpolation of 2D data, which I found useful for plotting, though it is not adequate ...
143 views

### InterpolatingFunction::dmval error in the Piecewise function with an interpolation funcion included

I have a set of data, first I deal the data with an Interpolation function. excitef1 = Interpolation[ps1] Then I use a Piecewise function to expand the range of ...
291 views

### calculate missing values, Interpolation

I've following data: ...
482 views

### Cosine interpolation

Suppose I have a list of values of a function $f(x)$ at positive integer points, say $$f(1) = -0.5, f(2) = -0.5, f(3) = 1, f(4) = -0.5, f(5) = -0.5, f(4) = 1,...$$ Can I interpolate a cosine function, ...
117 views

### Where do two bicubic-interpolated surfaces intersect a plane?

I have two surfaces, $p_a$ and $p_b$, described by two matrices. I want to find out if both surfaces intersect with the planes $q_a$ and $q_b$ respectively for any pair of x and y coordinates. To do ...
163 views

### Constructing a list

I need to use the interpolation function on some data so I can integrate it. I have an array with 1400 subsets and there are 1400 elements in each subset: ...
775 views

### How to create InterpolatingFunction from data?

If I have a function at a number of non-uniformly spaced data points: youtReal[7.8]=2.0332;, youtReal[8.54]=6.24352354;.................. ......... and the ...
92 views

### Motion study using initial conditions

I think I'm making a mistake to reach my goal. I would like to find an $x[t]$ function that could describe the following conditions: 1 - The object is in position $x=151$ (meters) at time $t=5$ (...
210 views

### Evaluate InterpolatingFunction of two variables on a 2D grid

I am using NDSolve to solve a system of pde's over a 2D domain: 2 equations and 2 unknowns which I call 'u' and 'v'. NDSolve returns an InterpolatingFunction for both 'u' and for 'v' and these are ...
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### Speeding up a minimisation involving Numeric integral and Interpolating function

I am doing a minimisation procedure to obtain best fit parameters a,b,NN for a model involving a numeric integral and an interpolation function. The code as written ...
489 views

### Interpolating noisy data

My data looks like this: https://pastebin.com/n59CTB3L Or if displayed in log chart: I want to create an interpolation of the data that would remove most of the noise. What are some good ways to ...
362 views

### How do I interpolate sparse data with a spline?

I have this data: data = {{0.2, 103}, {2, 13.9}, {20, 2.72}, {200, 0.8}, {2000, 0.401}, {20000, 0.433}} Is there any way of finding value at $x=5$ using ...
204 views

### Interpolation of non-rectangular data failed

I want to interpolate a type of data which is on a triangular lattice in order to make DensityPlot faster(ListDensityPlot is so slow). However, the interoplation failed with error, no matter setting <...
281 views

### Integrate only one variable of a 2D interpolating function

Lets say I have generated a 2D interpolating function using the code: ...
892 views

### Hermite interpolation

The well known Hermite interpolation uses piecewise cubic polynomials and fits the knot values and derivatives. In contrast the Mathematica piecewise Interpolation ...
72 views

### Line Equations from Interpolated Data

I have an interpolated line from a series of measured data points. Is there a way I can get Mathematica to output an approximate equation for the interpolated line? For example: From the ...
74 views

### Plotting continues field's properties by having some points information

Having information of a vector field in some discrete points in 2D space(points and vectors are both in 2D), how can one plots (approximate) divergence of the vector-field in the total space(not in ...
220 views

### Styling a ListLinePlot

Pretty new to mathematica and stack exchange, so feel free to explain it like i'm 5! Essentially, I have a (mostly) working ListLinePlot in Mathematica, but would like to change some things in the ...
84 views

### Functional derivatives of interpolated data

I have set of experimental data: points={{0, 0}, {1, 2}, {3, 3}, {4, 4}, {5, 3.5}, {6, 3}, {7, 2.5}, {8, 2}, {9, 1}, {10, 0}} and I would like: 1.) interpolate these points: fun = Interpolation[...
195 views

### Ways to quicken numeric integral over interpolating spline?

I have an integral of the form $$\int_1^{15000} f_1(k) f_2(k) dk,$$ where $f_1(k)$ is an interpolating function and $f_2(k)$ is some multiplicative function of k. I'm working with the following <...
806 views

### Cubic spline Interpolation [closed]

I'd like to fit a cubic spline object to some data in mathematica. I think I'm ok in how to set it up, I just need a little help with some of the syntax. I'd like to generate a list of data first ...