Numerical Methods implemented using numpy and matplotlib. For example usage, see below or see example.py.

(The name 'pryx' is somewhat of a mixture between 'python' and 'approx')

The contents of this repository are broken down by purpose into separate files. The different components are as follows

Contained within roots.py, Pyrx Roots contains pure-python implementations of common root-approximation methods including bisection, secant method, false position, and Newton's Method.

Bisection achieves guaranteed linear convergence for any function as long as it is given two points such that f(x) > 0 for one point and f(x) < 0 for the other. It is typically the slowest of the provided methods, but also the most stable, as it makes no assumptions about the nature of the function.

In the event that the given function has no zeros but a vertical asymptote or a jump discontinuity that crosses the x-axis, Bisection may find the point of discontinuity instead of a zero.

Secant method typically will converge faster than bisection, but in certain instances will not converge. In particular:

• The method may find two points x1 and x2 where f(x1) = f(x2), in which it cannot proceed
• The method may encounter a monotonic horizontal asymptote, in which case it will continue along the asymptote until timing out
• The method may get stuck in some kind of cycle in which it never arrives at a guess anywhere near the root.

For simple functions, these are unlikely circumstances, but they can occur.