steinerberger

steinerberger, an Octave 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.

Related Data and Programs:

steinerberger_test

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

polpak, an Octave 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:

• harmonic_number.m, computes the N-th harmonic number.
• steinerberger_function.m, evaluates the Steinerberger function.
• steinerberger_integral01.m, returns the Steinerberger integral from 0 to 1.