Unformatted text preview: Homework 4
1 A different kind of norms
1. Derive a version of the normal equations to minimize the M norm Let r(x) = Ax  b, then we can define the directional derivative of r2 as r2 d (x) = r(x + tu)2 M u dt where r(x + tu)2 = r(x) + tAu2 M M = r + tAu, r + tAu = r2 + 2t Au, r M + t2 Au2 M M so for t = 0, the original equation becomes 2 < Au, r >M = 2uT AT M (Ax  b) = 0 AT M (Ax  b) = 0 2. Show the 2norm form equivalence of the M form z2 = z T M z M = (z T L)(LT z) = (LT z)T (LT z) =0 t=0 1 ...
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This note was uploaded on 03/12/2012 for the course CS 3220 taught by Professor Marschner during the Spring '09 term at Cornell.
 Spring '09
 MARSCHNER

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