G22 : Scientific Computing

Ax is closest to b, when Ax-b ⊥ Ax

Lectures 2 & 3 : Ax = b

We want x, such that, Ax is as close to b as possible.

This happens when Ax-b ⊥ span(A)

I.E. Ax-b ⊥ Col1(A) , Ax-b ⊥ Col2(A) , ...

So, Ax-b · Col1(A) = 0, Ax-b · Col2(A) = 0, ...

AT(Ax-b) = 0

ATAx - ATb = 0

ATAx = ATb


Lecture 10 : Z=X+Y → fZ(z) = ΣₓP(z|x)*P(x) = ∫fY(z-x)*fX(x)dx = (fX★fY)(z)

N(μ₁,v₁)★N(μ₂,v₂)=N(μ₁+μ₂,v₁+v₂)