Closed root-finding methods - Executable Engineering: Interactive Numerical Methods in Python

import numpy as np
import plotly.graph_objects as go
from scipy.optimize import bisect

try:
    import executable_engineering as exe
except ImportError:
    %pip install -q executable_engineering
    import executable_engineering as exe

from executable_engineering import RootFinderClosed

Closed (Bracketting) methods¶

Closed iterative root finding methods (aka Bracketting methods) work when you can bound (bracket) the root, and therefore search through reducing the bounds until you’ve found it. Such methods are called closed because you will generally not wander off far from the root.

Bracketing methods exploits the fact that functions change sign across the roots of a 1-D function (a simple application of the intermediate value theorem). This does not work for some cases (eg: $1/x$ ) but are sometimes the only ones that will for others (Non-differentiable / pathological functions).: