NLA Visualizations

Arnoldi Iteration

Expanding the Krylov Subspace

AQk=Qk+1H~kA Q_k = Q_{k+1} \tilde{H}_k
Step 1 of 5
Step 1

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Expanding the Krylov subspace basis to dimension 1. Notice how Q_k has 1 column(s) while Q_{k+1} has 2 columns.

AA
0.50
-0.14
0.65
1.52
-0.23
-0.23
1.58
0.77
-0.47
0.54
-0.46
-0.47
0.24
-1.91
-1.72
-0.56
-1.01
0.31
-0.91
-1.41
1.47
-0.23
0.07
-1.42
-0.54
0.11
-1.15
0.38
-0.60
-0.29
-0.60
1.85
-0.01
-1.06
0.82
-1.22
×
QkQ_k
0.08
-0.78
-0.53
0.08
0.30
0.07
=
Qk+1Q_{k+1}
0.08
-0.04
-0.78
-0.41
-0.53
0.68
0.08
0.09
0.30
0.23
0.07
-0.55
×
H~k\tilde{H}_k
H_k
-0.86
2.45