steinerberger

steinerberger, a Python code which evaluates the Steinerberger functions f(n,x), which are continuous but have derivative discontinuities, are hard to accurately plot, interpolate, integrate, and minimize.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

steinerberger is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

fn, a Python code which approximates elementary and special functions using Chebyshev polynomials, by Wayne Fullerton.

polpak, a Python code which evaluates a variety of mathematical functions.

Reference:

1. John D Cook,
   Pushing numerical integration software to its limits,
   https://www.johndcook.com/blog/2023/06/12/stressing-numerical-integration/
   Posted 12 June 2023.
2. John D Cook,
   Plotting a function with lots of local minima,
   https://www.johndcook.com/blog/2023/06/12/lots-of-local-minima/
   Posted 12 June 2023.
3. Stefan Steinerberger,
   A amusing sequence of functions,
   Mathematics Magazine,
   Volume 91, Number 4, October 2018, pages 262-266.

Source Code:

• steinerberger.py, the source code.
• steinerberger.sh, runs all the tests.
• steinerberger.txt, the output file.

• steinerberger_01.png
• steinerberger_05.png
• steinerberger_10.png
• steinerberger_25.png
• steinerberger_50.png
• steinerberger_100.png