Question

Problem 2 Consider the causal non-linear discrete-time system characterized by the following difference equation: 2y[n] yn-1]+x[n] /yn-] If we use as input x[n] to this system (algorithm) a step function of amplitude P (i.e. xIn]-P u[n]), then y[n] will converge after several iterations to the square root of P .Write a MATLAB program that implements the above recursion to compute the square . How many iterations does it take to converge to the true value starting at y[-1]-0.2? roots of 25, 9, 3, and 2

Answer 1

MATLAB code is given below in bold letters.

clc;
clear all;
close all;

% Define intial conditions
y(1) = 0.2;
n = 2;
count1 = 0; % Number of iterations

a = input('Enter x: ');
x = a*ones(1,1e5);

while(1)
y(n) = 1/2*(y(n-1)+x(n)/y(n-1)) ;
error = sqrt(x(n))-y(n);
count1 = count1+1;
if abs(error)<0.0001 % accuracy upto 4 decimal places
break;
end
n = n+1;
end
fprintf('Square root of %1.0f is %1.5f \n',x(n-1),y(n-1));
fprintf('Number of iterations is %1.0f \n',count1);

RESULT:

Enter x: 25
Square root of 25 is 5.00036
Number of iterations is 8

Enter x: 9
Square root of 9 is 3.00117
Number of iterations is 7

Enter x: 3
Square root of 3 is 1.73412
Number of iterations is 6

Enter x: 2
Square root of 2 is 1.41453
Number of iterations is 6