bv_cvxbook_extra_exercises

# Show that if f is log concave then the maximum

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Unformatted text preview: d for k = 4 and Ω = [−0.6, −0.3] ∪ [0.7, 1.8]. You can replace the supremum of a polynomial over Ω by a maximum over uniformly spaced (within each interval) points in Ω, with spacing 0.01. Give the optimal value Rwc⋆ and the optimal coeﬃcients c⋆ = (c⋆ , . . . , c⋆ ). 0 k Remarks. (Not needed to solve the problem.) 50 • The approximate inverse p(A)b would be computed by recursively, requiring the multiplication of A with a vector k times. • This approximate inverse could be used as a preconditioner for an iterative method. • The Cayley-Hamilton theorem tells us that the inverse of any (invertible) matrix is a polynomial of degree n − 1 of the matrix. Our hope here, however, is to get a single polynomial, of relatively low degree, that serves as an approximate inverse for many diﬀerent matrices. 5.17 Fitting a generalized additive regression model. A generalized additive model has the form n fj ( x j ) , f (x) = α + j =1 for x ∈ Rn , where α ∈ R is t...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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