eliminating x from the rst equation gives an

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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 substitution step). 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 minimize 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....
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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 Berkeley.

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