GATE | GATE CS 2008 | Question 85

The Newton-Raphson iteration  can be used to compute the.
(A) square of R
(B) reciprocal of R
(C) square root of R
(D) logarithm of R


Answer: (C)

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.

Source: http://www.cse.iitd.ac.in/~mittal/gate/gate_math_2008.html

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