Using Matlab Carry out 50 steps of the power method for the

Using Matlab,

Carry out 50 steps of the power method for the matrix A = [2 -1 0 3 1 -1 1 1 0 2 1 -2 1 0 1 1]with X_0 = [1, 1, 0, 2]. Give your estimate for the dominant eigenvalue lambda from x: = X_49 and y: = y_49 = AX_49 via lambda = lambda = y_i/x_i where |x_i| = max_j |x_j|.

Solution

code:

function [m,y]=power_method(A,x,steps)

% A input matrix
%x initial vector x0
% steps number of steps
% y_final normalized eigen vector

m=0;
n=length(x);
y=x;
total_steps=steps;
i=0;
while(i~=total_steps)
mold = m;
y_old=y;
y=A*y;
m=max(y);
y=y/m;
i=i+1;
end
end

output

>> A

A =

2 -1 0 3
1 -1 1 1
0 2 1 -2
1 0 1 1

>> x

x =

1
1
0
2

>> steps

steps =

50

>> [m y]=power_method(A,x,steps)

m =

3

y =

1.0000
0.3333
-0.1111
0.4444

>>