Page 233 - MATLAB an introduction with applications

218 ——— MATLAB: An Introduction with Applications

Matrix in tridiagonal form is

4.0000 –3.7417 0 0
–3.7417 14.5714 2.6245 0
0 2.6245 2.6878 –0.7622
0 0 –0.7622 2.7407
Example E4.4: Use the QR factorization method with Householder transformation to calculate the eigen-
values and the corresponding eigenvectors of the matrix [K], where
 5 − 4 1 0 
 − 4 6 − 4 1 
[] =  
K
 1 − 4 6 − 4 
 
  0 1 − 4 5  
Solution:
MATLAB Solution [Using built-in function]:
>> A = [5 – 4 1 0; – 4 6 – 4 1; 1– 4 6 – 4; 0 1 –4 5];
>> kmax = 200;
>> [eigs,A] = eig_QR(A, kmax)
eigs =
13.0902
6.8541
1.9098
0.1459
A =
13.0902 0.0000 0.0000 –0.0000
–0.0000 6.8541 0.0000 0.0000
0.0000 –0.0000 1.9098 0.0000
0 0 –0.0000 0.1459
>> A = [5 – 4 1 0; – 4 6 – 4 1;1 – 4 6 – 4;0 1 – 4 5];
>> [Q,d] = eig(A)
Q =
– 0.3717 – 0.6015 0.6015 – 0.3717
– 0.6015 – 0.3717 – 0.3717 0.6015
– 0.6015 0.3717 – 0.3717 – 0.6015
– 0.3717 0.6015 0.6015 0.3717
d =
0.1459 0 0 0
0 1.9098 0 0
0 0 6.8541 0
0 0 0 13.0902