steinerberger

steinerberger, a MATLAB 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 computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

steinerberger is available in a MATLAB version.

Related Data and Programs:

steinerberger_test

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

polpak, a MATLAB 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.