bv_cvxbook_extra_exercises

Show that if f is log concave then the maximum

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online