MATLAB Program to find out Square root by solving Difference equation
Consider the
causal non-linear
discrete-time system
characterized
by
the following difference equation:
2y[n] = y[n-1] + x[n]/y[n-1]
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 81,
49, 16 and 3.
·
How
many iterations does
it take to converge to the true value
starting
at
y[-1] = 0.2?
MATLAB Code
function [yn,iter] = squareroot2(A,yminus1)
yn=0.5*((yminus1)+A/yminus1);%running the
first iteration outside the loop
yminus1 = yn;%taking the initial value for
next iteration
iter=1;
while yn~=sqrt(A)%loop stops when square root
found
yn=0.5*((yminus1)+A/yminus1);
yminus1 = yn;
iter=iter+1;
end
end
Output
(MATLAB)
[sqrt2,iterations]=squareroot2(81,0.2)
sqrt2 =
9
iterations =
10
[sqrt2,iterations]=squareroot2(49,0.2)
sqrt2 =
7
iterations =
10
[sqrt2,iterations]=squareroot2(16,0.2)
sqrt2 =
4
iterations =
9
[sqrt2,iterations]=squareroot2(3,0.2)
sqrt2 =
1.7321
iterations =
8
