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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.

 ⁕ When the Newton's Method go wrong?

↪ 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

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