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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 ( e , f ) ∂f ∂f q = m i =1 ( k i + e i )( 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 ( e , f ) = D 2 e F T r ( K + E ) T r , H ( e , f ) = D 2 + F T F R T + F T ( K + E ) R + ( K + E ) T F ( K + E ) T ( K + E ) . The Newton direction is the solution to H ( e , f ) p = g . CHALLENGE 15.3. The least squares problem is of the form min x Ax b 2 , where x = Δ 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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