GATE | GATE CS 2008 | Question 85

The Newton-Raphson iteration 

 can be used to compute the.

(A)

square root of R 

(B)

logarithm of R

(C)

reciprocal of R

(D)

square of R 

Answer: (A)
Explanation:

According to Newton-Raphson method, 

xn+1 = xn − f(xn) / f′(xn) 

So we try to bring given equation in above form. Given equation is : 

xn+1 = xn/2 + R/(2xn) 
    = xn − xn/2 +  R/(2xn) 
    = xn − (xn2 − R2)/(2xn) 

So clearly f(x) = x² − R, so root of f(x) means x² − R = 0 i.e. we are trying to find square root of R. So option (C) is correct.

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