Write a wellcommented MATLAB function program mypm that inpu

Write a well-commented MATLAB function program ‘mypm’ that inputs a matrix and a tolerance, applies the power method until the change in the vector is less than the tolerance, and outputs the number of steps used and the largest estimated eigenvalue. Test your program on the matrix B

-2 0 1 B=11-2 0 -2

Solution

Main_Prog:

clc;
clear all;
close all;
A = input(\'Enter the Matrix:\'); %Reading matrix from command window
tolerance = input(\'Enter the Tolerance:\');%Reading tolerance value from command window
[vec,val,j] = mypm(A,tolerance);% Calling \"mypm\" function by providing input matrix and tolerance
disp(\'The Eigen Value is:\');
disp(val); % Displaying the Dominant Eigen Value in command window
disp(\'The no. of iterations are:\');
disp(j); % Displaying the No. of iterations in command window

Function Program \'mypm\':

%Power method for computing eigenvalues
function [vector,value,i]=mypm(B,tolerance) % Creatinf function program \'mypm\'
x = [1;1;1]; % Start matrix for initial approximation
dd=1;% Maximum tolerance allowed
n=10;% Initial assumption of dominant eigen vector
i=0;% Initialization for calculating no. of iterations
while dd > tolerance % Checking the condition for change in the vector is less than the tolerance
y=B*x
dd=abs(norm(x)-n);
n=norm(x)
x=y/n
i = i+1; % Final total No. of iterations
end
vector=x;% final dominant eigen vector
value=n;% final dominant eigen vector

Output in command window:

Enter the Matrix:[-2 1 0;1 -2 1;0 1 -2]
Enter the Tolerance:0.1

y =

-1
0
-1

n =

1.7321

x =

-0.5774
0
-0.5774

y =

1.1547
-1.1547
1.1547

n =

0.8165

x =

1.4142
-1.4142
1.4142

y =

-4.2426
5.6569
-4.2426

n =

2.4495

x =

-1.7321
2.3094
-1.7321

y =

5.7735
-8.0829
5.7735

n =

3.3665

x =

1.7150
-2.4010
1.7150

y =

-5.8310
8.2319
-5.8310

n =

3.4128

x =

-1.7086
2.4121
-1.7086

The Eigen Value is:
3.4128

The no. of iterations are:
5