bv_cvxbook_extra_exercises

# Remark for your amusement only the isoperimetric

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ose to the boundary of the unit disk. (Please turn in this plot, and give us the values of αj that you ﬁnd.) The function polyval may be helpful. Remarks. • We’ve been a little informal in our mathematics here, but it won’t matter. • You do not need to know any complex analysis to solve this problem; we’ve told you everything you need to know. • A basic result from complex analysis tells us that ϕ is one-to-one if and only if the image of ˆ the boundary does not ‘loop over’ itself. (We mention this just for fun; we’re not asking you to verify that the ϕ you ﬁnd is one-to-one.) ˆ 7.12 Fitting a vector ﬁeld to given directions. This problem concerns a vector ﬁeld on Rn , i.e., a function F : Rn → Rn . We are given the direction of the vector ﬁeld at points x(1) , . . . , x(N ) ∈ Rn , q (i) = 1 F ( x (i) ) F ( x (i) ) , i = 1, . . . , N. 2 (These directions might be obtained, for example, from samples of trajectories of the diﬀerential equation z = F (z ).) The goal is to ﬁt these samples with a vector ﬁeld of th...
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