Differential Equations Solutions 75

Differential Equations Solutions 75 - 85 Retaining 12...

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85 1 2 3 4 5 -1 0 1 2 3 4 Retaining 12 singular values 1 2 3 4 5 -1 0 1 2 3 4 Retaining 15 singular values 1 2 3 4 5 -1 0 1 2 3 4 Retaining 17 singular values 1 2 3 4 5 -1 0 1 2 3 4 5 Retaining 21 singular values Figure 14.1. Computed least squares solutions (counts vs. energies) for various values of the cutoF parameter ˜ n . ˜ σ 2 n +1 ± ˜ f ± 2 2 = n +1 i =1 ˜ σ 2 n +1 ˜ f 2 i n +1 i =1 ˜ σ 2 i ˜ f 2 i = ± ˜ Σ ˜ f ± 2 2 Therefore, ˜ σ n +1 ± ˜ f ± 2 ≤± ˜ Σ ˜ f ± 2 = ± ˜ E ˜ f ± 2 ≤± ˜ E ± 2 ± ˜ f ± 2 ≤± ˜ E ± F ± ˜ f ± 2 ,sow e conclude that ± ˜ E ± F ˜ σ n +1
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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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