The gravitational potential energy of the ith mass is

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Unformatted text preview: 1F 0 −I ∈ R(n+k)×(1+k) , treating it as dense, ignoring the (little) exploitable structure in it. (c) Carry out your method from part (b) on some randomly generated data with dimensions n = 2500, k = 30. For comparison (and as a check on your method), compute the optimal portfolio using the method of part (a) as well. Give the (approximate) CPU time for each method, using tic and toc. Hints. After you generate D and Q randomly, you might want to add a positive multiple of the identity to each, to avoid any issues related to poor conditioning. Also, to be able to invert a block diagonal matrix efficiently, you’ll need to recast it as sparse. (d) Risk return trade-off curve. Now suppose we want to compute the optimal portfolio for M values of the risk aversion parameter λ. Explain how to do this efficiently, and give the complexity in terms of M , n, and k . Compare to the complexity of using the method of part (b) M times. Hint. Show that the optimal portfolio is an affine function of 1/λ. 113 13.15 Sparse index tracking. The (weekly, say) return of...
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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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