I’m creating a program for finding the square root of a number, and I came across the Newton-Raphson method, an algorithm that solves my task.
I only saw the pseudocode for the algorithm, but I never really understood why it worked. Can someone explain to me why it works without all the heavy math?
In: Mathematics
It’s using the derivative as an approximation of the line between the current guess and the zero of the function.
If you think of a line representing a function, square root in your example, and a current guess (X), then the derivative of the function represents the slope at X. This slope is a line that crosses the zero axis, and since it’s a straight line the crossing point is easy to calculate. That zero point is a better guess for the zero than X, so if you start from that point and iteratively repeat the process you can get very close to the actual zero very quickly.
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