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Sahithyan's S2
Sahithyan's S2 — Methods of Mathematics

Newton's Method

A special case of fixed point method.

Given a root finding problem f(x)=0f(x)=0, g(x)g(x) is defined as:

g(x)=xf(x)f(x)g(x) = x - \frac{f(x)}{f'(x)}

Start with an arbitrary point p0p_0 and generate the sequence: pn=g(p0)p_n = g(p_0). The sequence pnp_n approaches the root of ff quickly.

Order of convergence is 2 for simple roots.