Newton-Raphson's Method
↪ The Newton-Raphson’s Method or Newton’s Method is a powerful technique for solving equations numerically. ↪ Let f(x) be a well-behaved function and let x be a root of the equation f(x) = 0. We st...
Newton's Method of Finding Square Root
Let x2 = a and f(x) = x2 – a. Here we know the root exactly, so we can see better how well the method converges.
We have,
This relation is known as Newton's iteration equation.
↪ Newton's method stops if f '(xn) = 0 at some level of iteration. Then the method has to be started with another initial guess.
⁕ Drawbacks of Newton Raphson's Method
↪ Divergent at inflection points
↪ Initial guess cannot be a point at which first derivative is zero.
↪ Oscillation near local maximum and minimum.
↪Root jumping