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- by ♪⚝Sanjiv❀Jaiswal❁⩸ 3 months ago

Let x^{2} = a and f(x) = x^{2} – 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 '(x_{n}) = 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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