Differential Equations Solutions 73

Differential Equations Solutions 73 - i u i v T i , so...

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Chapter 14 Solutions: Case Study: Blind Deconvolution: Errors, Errors Everywhere CHALLENGE 14.1. See the posted program problem1 and 3.m . The program is not difficult, but it is important to make sure that you do the SVD only once (at acostof O ( mn 3 )) and then form each of the trial solutions at a cost of O ( n 2 ). This requires using the associative law of multiplication. In fact, it is possible to form each solution by updating a previous one (by adding the newly added term) at a cost of O ( n ), and this would be an even better algorithm, left as an exercise. CHALLENGE 14.2. (a) We know that £ Kg ¤ = n +1 X i =1 ˜
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Unformatted text preview: i u i v T i , so using the formula for E r we see that K g + E r = n X i =1 i u i v T i . Now, since v n +1 is orthogonal to v i for k = 1 , . . . , n , it follows that ( K g + E r ) f 1 = n X i =1 i u i v T i 1 v n +1 ,n +1 v n +1 = . Note that [ E , r ] F = n +1 . (b) This can be proven using the fact that A 2 F = trace( A T A ) where trace( B ) is the trace of the matrix B , equal to the sum of its diagonal elements (or the sum of 83...
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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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