What is the bisection method?
Understand the Problem
The question is asking about the bisection method, which is a numerical technique used to find roots of a function. It involves repeatedly bisecting an interval and selecting the subinterval in which the function changes sign, indicating the presence of a root.
Answer
A numerical method to find roots of continuous functions by interval splitting.
The bisection method is a numerical method used to find the roots of a continuous function by repeatedly splitting an interval and selecting the subinterval that contains the root.
Answer for screen readers
The bisection method is a numerical method used to find the roots of a continuous function by repeatedly splitting an interval and selecting the subinterval that contains the root.
More Information
The method is based on the intermediate value theorem which guarantees a root in an interval where the function changes sign. Due to its simplicity and robustness, the bisection method is widely used even though it can be slower compared to other numerical methods.
Tips
A common mistake is not ensuring that the values a and b have opposite signs before starting the algorithm. Always check that f(a) and f(b) have opposite signs.
Sources
- Bisection Method - Wikipedia - en.wikipedia.org
- Bisection Method: Numerical Method for finding Roots with Examples - testbook.com
- Bisection Method - Python Numerical Methods - pythonnumericalmethods.studentorg.berkeley.edu
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