Bisection Method

# Bisection Method

## An Introduction to Bisection Method

The bisection method is a numerical method used to solve equations. The method works by dividing the interval containing the root of the equation into two equal parts and then solving the equation in each half. An Introduction to Bisection Method.

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The algorithm is as follows:

1. Choose a starting point in the interval.

2. Find the midpoint of the interval.

3. If the function is decreasing on one side of the midpoint and increasing on the other side, the root lies in the half-open interval on the side of the function that is increasing.

4. If the function is increasing on one side of the midpoint and decreasing on the other side, the root lies in the half-open interval on the side of the function that is decreasing.

5. If the function is constant on one side of the midpoint and not constant on the other side, the root lies in the half-open interval on the side of the function that is not constant.

6. Repeat steps 2-5 until the root is found.

## Finding Root by Bisection Method

To find the root of a function using the bisection method, we first need to find a function that can be accurately approximated by a linear function near the root. We then use the bisection algorithm to find the root of the function.

The bisection algorithm works by finding the midpoint of the interval that contains the root and then splitting the interval in half. We then repeat this process until the interval is small enough that the root can be found accurately.

## Bisection Method Procedure

The bisection method is a numerical procedure that is used to find the roots of a function. The roots are the points where the function equals zero. The bisection method works by dividing the interval of possible solutions in half and then checking to see which half contains the root. The bisection method is a simple, but efficient, way to find the roots of a function.

## Advantages of Bisection Method

Bisection Method is easy to understand and implement.

The bisection method is a fast and reliable algorithm for solving equations.

The bisection method is an iterative algorithm, so it can be stopped anytime when the required accuracy is reached.

No round-off errors are introduced by the algorithm.

## Disadvantages of Bisection Method

The bisection method can be slow if the function is not continuous.

## Bisection Method Problems

A bisection method is a type of root-finding algorithm. It is used to find the roots of a function by finding the points where the function is equal to zero. The bisection method is a simple and efficient algorithm, but it can only be used to find the roots of a function that is continuous and has a single root.

Bisection Method.

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