The following are solutions to the Hundred-dollar, Hundred-digit Challenge problems posed by Professor Nick Trefethen - various mathematical problems where the goal is to provide an answer to within 10 digits of accuracy. The solutions are implemented in Python as well as using additional scientific computing libraries (e.g. numpy, scipy, sympy for symbolic calculation, mpmath for extended precision). Originally, these started as a final project for a class on Computational Mathematics, but I ended up continuing it after the class ended. For many of the problems, in order to get sufficiently high accuracy, a combination of mathematical enginuity as well as good implementation of efficient algorithms are needed.
Many of the approaches and exposition used follow the book written by some of the original contest’s participants: The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing