The Bisection method is a method used in mathematics that helps an individual find the square root of an equation. This method revolves around using transcendental equations instead of polynomial equations. The difference between the two being transcendental equations satisfy equations that aren’t algebraic whereas an algebraic equation is satisfied by a polynomial function. There are both upsides and downsides to this method, which I’m going to outline in the following content.
Pros of Bisection Method
1. Always Convergent.
The Bisection method is always convergent, meaning that it is always leading towards a definite limit. This is a positive thing because it means that the convergent sequence is guaranteed to show an individual the overall rate of convergence.
2. Easy to Understand.
The Bisection method is relatively simple compared to similar methods like the Secant method and the Newton-Raphson method, meaning that it is easy to grasp the idea the method offers.
3. It is Fault Free (Generally).
The great thing about the Bisection method is that it is an extremely reliable method. If you have values (a) and (b), which bracket a single zero, then there isn’t any way that you won’t gain the answer you need.
Cons of Bisection Method
1. Rate of Convergence is Slow.
This is the greatest drawback of the Bisection method, it is very slow. Relative to other methods that help you identify the square root of an equation, the Bisection method is extremely slow. Although it isn’t significantly inefficient if you are only finding zeros of a function a hand full of times, there are instances where an individual needs to find zeros of a function thousands of times. During these instances the Bisection method is simply to slow and time consuming.
2. Relies on Sign Changes.
If there are no sign changes whilst the method is in practice, then the method will be incapable of finding any zeros.
3. Can’t Detect Multiple Roots.
The Bisection method fails to identify multiple different roots, which makes it less desirable to use compared to other methods that can identify multiple roots.
4. Requires a Lot of Effort.
Although the Bisection method is very reliable, it is inefficient compared to other methods such as the Newton-Raphson method. A lot of hard work and a higher quantity of iterations is needed to find a high level answer, compared to various other methods that help you find a similar answer with much less work.