Differential Equations Solutions 80

Differential Equations Solutions 80 - 90 Chapter 15....

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90 Chapter 15. Solutions: Case Study: Blind Deconvolution: A Matter of Norm ∂F ( b e , f ) ∂f ± q = m X i =1 ( k + e )( k iq + e iq )=(( K + E ) T ( K + E )) ±q , where out-of-range entries in summations are assumed to be zero and R is a matrix whose nonzero entries are components of r .So g = F ( b e , f )= · D 2 b e F T r ( K + E ) T r ¸ , H ( b e , f · D 2 + F T FR T + F T ( K + E ) R +( K + E ) T F ( K + E ) T ( K + E ) ¸ . The Newton direction is the solution to H ( b e , f ) p = g . CHALLENGE 15.3. The least squares problem is of the form min x ± Ax b ± 2 , where x = · Δ b e Δ f ¸ and A and b are the given matrix and vector. So to minimize ± Ax b ± 2 =( Ax b ) T ( Ax b ), we set the derivative equal to zero, obtaining A T Ax A T b = 0 . The solution to this equation is a minimizer if the second derivative
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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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