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
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.