Differential Equations Solutions 77

Differential Equations Solutions 77 - 87 Lcurve for TLS...

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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 L-curve for TLS Figure 14.4. The L-curve 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 well-conditioned matrix ! Most spectroscopy problems have a very ill-conditioned matrix. (An ill-conditioned 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.

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