87
10
2
10
1
10
0.9
10
0.91
10
0.92
10
0.93
10
0.94
10
0.95
10
0.96
10
0.97
residual norm
solution norm
Lcurve for TLS
Figure 14.4.
The Lcurve for total least squares solutions.
other components should have at least some data in addition to noise. Therefore,
estimate the variance using the last 5 to get
δ
2
=1
.
2349
×
10
−
4
.
The condition number of the matrix, the ratio of largest to smallest singular
value, is 61
.
8455. This is a
wellconditioned matrix
! Most spectroscopy problems
have a very illconditioned matrix. (An illconditioned one would have a condition
number of 10
3
or more.) This is a clue that there is probably error in the matrix,
moving the small singular values away from zero.
We try various choices of ˜
n
, the number of singular values retained, and show
the results in Figure 14.1 (blue solid curves). The discrepancy principle predicts the
res
idua
lnormtobe
δ
√
m
=0
.
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.
 Fall '11
 Dr.Robin

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