About the Newton-Raphson Method

The Newton-Raphson method was named after Newton and Joseph Raphson. This method, also known as the tangent method, considers tangents drawn at the initial approximations, which gradually lead to the real root.

Algorithm

1. Get the function f(x), initial value(x_i), and the maximum error percent(e) of the root as an input
2. Get the derivation f(x)
3. With a given initial value(x), compute the value of f(x) and its derivative f'(x)
4. With the formula: x_i+1 =x_i-^f(x_i)⁄_f'(xi) , compute for the succeeding approximate root
5. Solve for the approximate percent relative error (∈_∝). ∈_∝ =|^{x_i+1- x_i⁄}_xi+1| 100%.
6. If the is ∈ > e,   set x = x_{i + 1}   go back to step 4 else, x_{i + 1} is the approximate root

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