# Algorithm and Flowchart For Bisection Method

## Algorithm and Flowchart For Bisection Method

Let us learn the flowchart for bisection method along with the bisection method algorithm.

#### What is Bisection Method?

The bisection method is a root-finding method, where, the intervals i.e., the start point and the end point are divided to find the mid point.

After bisection, a subinterval is selected in which the root should lie. As said, the bisection method requires two initial guesses. The bisection method is based on Intermediate value theorem.

The bisection method is used to solve transcendental equations and is a closed bracket method. The bisection method is also known as:

- Binary search method
- Internal halving method
- Dichotomy method

The bisection method is used to find the real roots of a non-linear function. The bisection method guarantees linear convergence but it takes a lot of time as compared to other methods.

#### Bisection Theorem

An equation f(x)=0, where f(x) is a real continuous function, has at least one root between a and b, if f(a) f(b) < 0.

**Must Read: C Program for Bisection Method**

#### Flowchart For Bisection Method

#### Algorithm of Bisection Method

Let us try to understand the bisection method algorithm.

- Input two values for f(a) and f(b).
- Find the mid-point value of the function.
- If the transformation is satisfactory, return the mid-point and then stop the iteration.
- Check the sign value of f(c) and replace the appropriate function and values.

**Pseudocode for Bisection method Algorithm**

1 2 3 4 5 6 | Do midpoint = (start_interval + end_interval) / 2 if(f(start_interval) * f(midpoint) < 0) then end_interval = midpoint else(start_interval = midpoint) while(none of the convergence criteria is satisfied) |

#### Bisection Method Example

Find the root of f(x) = x^{3} – 4.

Let a = 1, b = 2 and absolute error = 0.5.

f(1) = 1 − 4 = −3

f(2) = 8 − 4 = 4

f(1.5) = 3.3750 − 4 = -0.6250

Incrementation and modifications may be required in case the root does not seem to match properly. Hence, there are quite a few disadvantages of the bisection method.

#### Advantages of Bisection Method

- The bisection method will ensure convergence at any given condition.
- The root brackets get halved with each iteration which is also guaranteed.
- The bisection algorithm is the simplest of all the other related algorithms.

#### Drawbacks of Bisection Method

- Linear convergence is slower compared to other methods.
- Two initial guesses are required i.e., f(a) and f(b) which should be less than zero.
- A lot of iterations are required when compared with other methods.
- The bisection method cannot find complex roots of polynomials.

If you have any doubts or additional points on flowchart for bisection method algorithm, do let us know about your views in the comment section below. Check **wikipedia** for more information.

Thanks. But, I belive this algorithm of bisection method is very slow. You must use others such as Newton raphson method.