Question

One old-time method to estimate the square root of any positive number a is called divide and average: xi+1 = xi + a xi 2 Show that this formula is equivalent to Newton method. Hint: Start by solving f (x) = x 2 − a = 0. Use Matlab code

Answer 1

MATLAB CODE

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clc;
clear all;
a=10; % Write number a whose square root is to be evaluated
f=@(x) x^2-a ; % Function
f1=@(x) 2*x; % Derivative of the function
x(1)=1; % Initial guess

for i=1:1:100
x(i+1)=x(i)-(f(x(i))/f1(x(i)));
err=abs(x(i+1)-x(i));
if ( err <0.0001 )
root=x;
break
end
end
SQroot=x(i+1)

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OUTPUT:

SQroot =

3.1623