Description: The Bisection Method is a numerical algorithm used to find roots of continuous functions. This method is based on the intermediate value theorem, which states that if a function is continuous on a closed interval and changes sign at its endpoints, then there is at least one root in that interval. The technique involves repeatedly dividing the interval in half and evaluating the function at the midpoint. Depending on the sign of the function at this point, it is determined in which of the two halves the root lies, discarding the other half. This process is repeated until a desired level of precision is reached. The Bisection Method is particularly valued for its simplicity and robustness, as it always converges to a solution, provided the initial conditions are met. However, its convergence speed is slower compared to more sophisticated methods, such as the Newton-Raphson method. Despite this, its ease of implementation and ability to guarantee a solution make it a popular choice in numerical analysis and applications where root-finding is required.
