AIR Tools - A MATLAB Package for Algebraic Iterative ...

2.2 SVD and Picard Condition 7
U(:,k)
U(:,k)
U(:,k)
0
−0.2
k = 1
−0.4
0 50
n
k = 4
0.5
0
−0.5
0 50
n
k = 7
0.5
0
−0.5
0 50
n
U(:,k)
U(:,k)
U(:,k)
0.5
0
k = 2
−0.5
0 50
n
k = 5
0.5
0
−0.5
0 50
n
k = 8
0.5
0
−0.5
0 50
n
U(:,k)
U(:,k)
U(:,k)
0.5
0
k = 3
−0.5
0 50
n
k = 6
0.5
0
−0.5
0 50
n
k = 9
0.5
0
−0.5
0 50
n
Figure 2.1: The first 9 left singular vectors ui for the test problem shaw.
10 5
10 0
10 −5
10 −10
10 −15
Picard Plot with b exact
σ
i
T
|u b|
i
T
|u b|/σi
i
10
0 10 20 30 40 50
−20
i
(a) Picard plot with no noise.
10 20
10 10
10 0
10 −10
Picard Plot with b noise
σ
i
T
|u b|
i
T
|u b|/σi
i
10
0 10 20 30 40 50
−20
i
(b) Picard plot with noise.
Figure 2.2: The Picard plot for the test problem shaw. The left figure is with no noise
while the right figure is with noise level δ = 10 −3 .