8 votes

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/...
Henrik Schumacher's user avatar
8 votes

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. ...
user444's user avatar
  • 2,126
7 votes
Accepted

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 "...
Michael E2's user avatar
  • 234k
7 votes

InterpolationOrder creates a sharp valley even if I increase the number of points. How to have a smooth curve?

modified Try Method -> "Hermite" ...
Ulrich Neumann's user avatar
7 votes

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 ...
Daniel Huber's user avatar
  • 49.9k
7 votes
Accepted

Find the zero crossing in data

$Version "13.3.0 for Microsoft Windows (64-bit) (June 3, 2023)" ...
cvgmt's user avatar
  • 69.3k
7 votes

Volume of Region Contained by 3D Data Points

Volume under the surface ...
Greg Hurst's user avatar
  • 35.8k
6 votes
Accepted

How can I write the equation of the parabola passing through list of three points?

Lagrange interpolating polynomials are implemented in Mathematica as the InterpolatingPolynomial function. The Lagrange interpolating polynomial is the polynomial ...
creidhne's user avatar
  • 4,930
6 votes

Precision of interpolation function after exporting and importing

This reproduces the behavior without using Export or Import: ...
Goofy's user avatar
  • 2,582
5 votes
Accepted

Remove spikes and dips in a spline function

Sometimes it helps to evenly space your data before interpolation: Let's first look at the successive spacings between your data points: ...
ydd's user avatar
  • 3,653
5 votes
Accepted

How to produce the following table faster?

Here's an attempt to improve further upon @HenrikSchumacher's excellent answer: ...
Lukas Lang's user avatar
  • 33.6k
5 votes

How can I write the equation of the parabola passing through list of three points?

We can define a Lagrange polynomial of order 2: ...
Roman's user avatar
  • 46.9k
5 votes

Shape of a boomerang

Based on @user84456's helpful answer we can evaluate the parameters needed for the simulation (see my comment ) ...
Ulrich Neumann's user avatar
5 votes
Accepted

Integrate InterpolatingFunction times polynomial

An "exact" result instead of an approximation by FunctionInterpolation: ...
Goofy's user avatar
  • 2,582
5 votes

How to tell NDSolve to suppress creation of interpolation function on successful exit?

You can tell NDSolve to only return the final value instead of an interpolation over the time interval, as noted in the NDSolve documentation (2nd line of Details section). For example: ...
tad's user avatar
  • 1,855
4 votes
Accepted

How to speedup integration of interpolated function with logarithmized data?

I suggest that you try to use the substitution formula: $$ \int_a^b \int_c^d f( \varphi(x),\psi(y)) \, \varphi'(x) \, \psi'(y) \, \mathrm{d}x \, \mathrm{d}y = \int_{\varphi(a)}^{\varphi(a)} \int_{\psi(...
Henrik Schumacher's user avatar
4 votes

FindPeaks in a 2d list and half values

...
Alan's user avatar
  • 13.7k
4 votes

How to correctly extrapolate function?

...
Bob Hanlon's user avatar
  • 155k
4 votes

Does FunctionRange work with Interpolation?

With Carl Woll's InterpolationToPiecewise: ...
Michael E2's user avatar
  • 234k
4 votes

How can I write the equation of the parabola passing through list of three points?

...
eldo's user avatar
  • 60.9k
4 votes
Accepted

Solving A System of Two Implicit Equations

First plot the function you want tointerpolate ...
Ulrich Neumann's user avatar
4 votes
Accepted

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 ...
eldo's user avatar
  • 60.9k
3 votes
Accepted

Plotting Polar Solution of NDSolve

Knowing the parametrized solutions r[t] an theta[t], we can transform them to Cartesian coordinates and use ParametricPlot: ...
Daniel Huber's user avatar
  • 49.9k
3 votes
Accepted

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 ...
lericr's user avatar
  • 26.4k
3 votes

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 ...
Roland F's user avatar
  • 3,263
3 votes

How can I interpolate a piecewise constant function?

For functions your can directly use FunctionInterpolation[ ] like this ...
Acus's user avatar
  • 3,669
3 votes

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: ...
bill s's user avatar
  • 68.8k
3 votes

Volume of Region Contained by 3D Data Points

Just to illustrate closeness of other answers to analytic answer for this volume of revolution: ...
ubpdqn's user avatar
  • 60k
3 votes
Accepted

Artifacts when interpolating on an unstructured set of 3D data

How about something like this: ...
user21's user avatar
  • 39.4k
3 votes

How to interpolate an implicit function?

Clear[chi, eq, t] eq[chi_, t_] := 7/10*(t - 315)*(chi)^(10/16) + 8/1000*(chi)^(10/16 + 10/4)*1000^(10/4) - 1; Solve for chi ...
Bob Hanlon's user avatar
  • 155k

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