A textbook (likely the S.A. Bhatti book you shared earlier) explaining the Bisection Method. This is one of the most fundamental algorithms in Numerical Analysis for finding the “root” of an equation—essentially finding the value where a curve crosses the x-axis (f(x) = 0).
Since you are looking at the technical details now, here is a simplified breakdown of how this method works:
The Concept: “Divide and Conquer”
The Bisection Method is based on the Intermediate Value Theorem. If a continuous function $f(x)$ changes its sign (from positive to negative or vice versa) over an interval [a, b], there must be at least one root between a and b
Pros and Cons
- Pros: It is guaranteed to converge to a root if the function is continuous. It’s very simple to code in C++.
- Cons: it is slow compared to other methods like Newton-Raphson. It requires many iterations to get a very precise answer.