GATE | GATE-CS-2007 | Question 28
Consider the series Xn+1 = Xn/2 + 9/(8 Xn), X0 = 0.5 obtained from the Newton-Raphson method. The series converges to
As per Newton Rapson's Method, Xn+1 = Xn − f(Xn)/f′(Xn) Here above equation is given in the below form Xn+1 = Xn/2 + 9/(8 Xn) Let us try to convert in Newton Rapson's form by putting Xn as first part. Xn+1 = Xn - Xn/2 + 9/(8 Xn) = Xn - (4*Xn2 - 9)/(8*Xn) So f(X) = (4*Xn2 - 9) and f'(X) = 8*Xn
So clearly f(X) = 4X2 − 9. We know its roots are ±3/2 = ±1.5, but if we start from X0 = 0.5, according to equation, we cannot get negative value at any time, so answer is 1.5 i.e. option (A) is correct.
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