Math, asked by SushrutVinayak8090, 1 year ago

Find the rate of convergence of newton raphson method.

Answers

Answered by ryan567
0
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. 

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