# Tag Info

### How to produce the following table faster?

tl;dr: As always with my post, find the most recent implementation at the bottom of the post. InterpolationFunctions are indeed much less efficient than they could/...

### Shape of a boomerang

I do not clearly understand your question. However, if you want to plot the shape of a boomerang use the following code. ...
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### InterpolationOrder creates a sharp valley even if I increase the number of points. How to have a smooth curve?

First, hunting for a method that makes your data look nicer than standard methods looks suspicious, speaking as someone from outside science. That said, here's a standard method, Eugene Lee's "...
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### InterpolationOrder creates a sharp valley even if I increase the number of points. How to have a smooth curve?

modified Try Method -> "Hermite" ...
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### InterpolationOrder creates a sharp valley even if I increase the number of points. How to have a smooth curve?

You are creating the "valley" yourself by using polynomial interpolation. Polynomials always overshoot if the slope changes rapidly. What to do? You can ask yourself if high degree ...
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### Does FunctionRange work with Interpolation?

With Carl Woll's InterpolationToPiecewise: ...
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### Solving A System of Two Implicit Equations

First plot the function you want tointerpolate ...
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### Finding a specific value from interpolating function

To answer your first question: usol[t_, x_] := NDSolveValue[{D[u[t, x], x] == Sin[x], u[t, 0] == 0}, u[t, x], {x, 0, 10}] usol[1, x][[0]][1] 0.459698 ...
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### Plotting Polar Solution of NDSolve

Knowing the parametrized solutions r[t] an theta[t], we can transform them to Cartesian coordinates and use ParametricPlot: ...
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### Interpolation of date-time data to fill in missing data for data sources with different time resolution

If I've understood the question and comments, you could proceed as follows. Let's assume you have myTempData as a list of time-value pairs, where each time element ...
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### How to speedup the integration of a tabulated function?

By inspection the Transpose of your list consists of an immense data set of periodic step functions. First impression ...
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### How can I interpolate a piecewise constant function?

For functions your can directly use FunctionInterpolation[ ] like this ...
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### Conversion of an expression to function yields Tag Plus in ... is Protected error

The relevant part of your code appears to be: degree = 3; polyFunc = Total[Table[x^i, {i, 0, degree}]]; Now you want to make polyFunc into an actual function. Try: ...
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### Volume of Region Contained by 3D Data Points

Just to illustrate closeness of other answers to analytic answer for this volume of revolution: ...
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### Artifacts when interpolating on an unstructured set of 3D data

How about something like this: ...
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