Please solve the following equation using MATLAB , i\'m having a hard time under

Question

Please solve the following equation using MATLAB , i'm having a hard time undersanding it.(Please Paste the codes bellow all steps) ,I have to take my final exam in the next 48 hours.

Problem 2 Consider the causal non-linear discrete-time system characterized by the following difference equation: If we use as input x[n] to this system (algorithm) a step function of amplitude A (i.e. x[n]-A u[n]), then y[n] will converge after several iterations to the square root of A Write a MATLAB program that implements the above recursion to compute the square root of 8 49, 16 and 3. How many iterations does it take to converge to the true value starting at y-1]-0.2?

Explanation / Answer

% MATLAB program to implement the given iteration to compute the square root of 81,49,16 and 3.

function [sqrtX num_iteration] = sqrtX1(X,y_1)

yprev = y_1;%y[-1]
num_iteration = 1;
while 1 == 1
ynext = 0.5*((yprev)+(X/yprev));

if abs(yprev-ynext)<10^-4

sqrtX = ynext;
break;
else
yprev = ynext;
num_iteration = num_iteration+1;
      

        end
    end
end

Result displayed on command window:

>> sqrtX1(16,1)

ans =

4.0000

>> sqrtX1(4,1)

ans =

2.0000

>> sqrtX1(5,1)

ans =

2.2361

>> sqrtX1(3,1)

ans =

1.7321

>> [sqrtX, num_iteration] = sqrtX1(3,0.5)

sqrtX =

1.7321

num_iteration =

6

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