Find the rate of convergence of newton raphson method.
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Convergence of Newton-Raphson method:
Suppose  is a root of  and  is an estimate of  s.t. . Then by Taylor series expansion we have,

for some  between  and .
By Newton-Raphson method, we know that

i.e.

Using(2*) in (1*) we get

Say 
where  denote the error in the solution at n and (n+1) iterations.

ewton Raphson Method is said to have quadratic convergence.
Suppose  is a root of  and  is an estimate of  s.t. . Then by Taylor series expansion we have,

for some  between  and .
By Newton-Raphson method, we know that

i.e.

Using(2*) in (1*) we get

Say 
where  denote the error in the solution at n and (n+1) iterations.

ewton Raphson Method is said to have quadratic convergence.
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