Bi Section Method

Recall the statement of the intermediate value theorem.

Bi section method. Let f x be a continuous function on the interval. In mathematics the bisection method is a root finding method that applies to any continuous functions for which one knows two values with opposite signs. Find an appropriate starting interval.

It separates the interval and subdivides the interval in which the root of the equation lies. This method is used to find root of an equation in a given interval that is value of x for which f x 0. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign and therefore must contain a root.

If a function f x is continuous on an interval a b and f a f b 0 then a value c a b exist for which f c 0. Plug the value from step 2 into the function. Is based on the bolzano s theorem for continuous functions.

Calculates the root of the given equation f x 0 using bisection method. This method is suitable for finding the initial values of the newton and halley s methods. This method is applicable to find the root of any polynomial equation f x 0 provided that the roots lie within the interval a b and f x is continuous in the interval.

The bisection method also called the interval halving method the binary search method or the dichotomy method. The convergence to the root is slow but is assured. Use the bisection method to approximate the solution to the equation below to within less than 0 1 of its real value.

The principle behind this method is the intermediate theorem for continuous functions. This method is closed bracket type requiring two initial guesses. The method is also called the interval halving method the binary search method or the dichotomy method.