cs3220p4 - Homework 4 1 A different kind of norms 1 Derive...

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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 || r || 2 as || r || 2 ∂u ( x ) = d dt || r ( x + tu ) || 2 M t =0 = 0 where || r ( x + tu ) || 2 M = || r ( x ) + tAu || 2 M = h r + tAu, r + tAu i = || r || 2 M + 2 t h Au, r i M + t 2 || Au || 2 M so for t = 0, the original equation becomes
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