This preview shows page 1. Sign up to view the full content.
Unformatted text preview: nt point. Matlab will do the right thing, i.e., it will ﬁrst solve
L\g using forward substitution, and then it will solve -L’\(L\g) using backward substitution. Each
substitution is order n2 .
To fairly compare the convergence of the three methods (i.e., N = 1, N = 15, N = 30), the
horizontal axis should show the approximate total number of ﬂops required, and not the number
of iterations. You can compute the approximate number of ﬂops using n3 /3 for each factorization,
and 2n2 for each solve (where each ‘solve’ involves a forward substitution step and a backward
8.5 Eﬃcient numerical method for a regularized least-squares problem. We consider a regularized least
squares problem with smoothing,
n −1 k (a T x
i=1 − bi ) + δ n x2 ,
i 2 2 i=1 (xi − xi+1 ) + η i=1 n where x ∈ R is the variable, and δ, η > 0 are parameters.
(a) Express the optimality conditions for this problem as a set of linear equations involving x.
(These are called the normal equations....
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 Berkeley.
- Fall '13
- The Aeneid