APM1513 Assignment 3 solutions 2021 semester 1

APM1513

ASSIGNMENT 3




Question 1
give two commands

>rand("state",student_number);

>rand(1)



Run own output and paste your output here



Question 2
function x1 = powermethod(A, iter)

[m,n] = size(A);

x1=rand(n,1);

for k = 1 : iter

xcap = A*x1;

xnorm = norm(xcap,2);

x1 = xcap/norm(xcap,2);

end;

end


%A matrix

A = [2.781344 -1.921334 0.493612 1.367198 -1.014289; 0.015050 -0.205731 0.903377 1.780261 -
0.824057; -0.087144 0.606003 2.977860 -0.140473 -0.750938; 0.212440 -2.477599 0.980236
4.233562 -1.207581; -0.136646 -1.168924 0.453692 0.915245 1.712964 ];

% power method using Eigen values

x1 = powermethod(A,100);

eigVal_power_A = (A*x1)./x1;

% eigenvalues and eien vector values A*V = V*D

[V,D] = eig(A)

, Output

V =


0.4203 0.4864 -0.1081 0.3310 -0.4399
0.6126 0.2587 -0.4846 0.4498 0.2630
0.0040 0.4096 -0.0449 0.4752 0.8173
0.5710 0.3920 -0.8295 0.6533 0.1595
0.3493 0.6124 -0.2519 0.1884 0.2094



D =


1.0000 0 0 0 0
0 2.0000 0 0 0
0 0 2.5000 0 0
0 0 0 3.0000 0
0 0 0 0 3.0000



Question 3

function x1 = powermethod(A, iter)

[m,n] = size(A);

x1=rand(n,1);

for k = 1 : iter

xcap = A*x1;

xnorm = norm(xcap,2);

x1 = xcap/norm(xcap,2);

end;

end


%A matrix

A = [-1.6731385 -3.6381454 -1.8272855 -2.7022868; -1.7080530 -0.0039461 0.1019678 -1.3595453;
2.4426950 3.4321965 3.8982919 2.1372124; 5.7672696 5.4815125 1.3344020 6.2787928 ];

% power method using Eigen values

x1 = powermethod(A,100);

eigVal_power_A = (A*x1)./x1;