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Least Squares Problem Please Help

  1. Feb 22, 2007 #1
    Can someone help with the folowing?
    Suppose L1 is the line through the origin in the direction of a1 and L2 is the line through b in the direction of a2. I am supposed to find the closest points x1a1 and b+x2a2 on the two lines.

    So I am trying to find the equations that would minize ||x1a1-x2a2-b||.

    Not really sure what equations to write. I know that I'm trying to find some vector c so that (c-x1a1+x2a2+b)^2 will be the minimum. This means that if I take the derivative of the above, then the derivative will be zero. So, if I break c down into its components, would I get

    2(c1-x1a1)+2(c2+x2a2+b)=0? Or, would I be trying to find the projection of x2a2+b onto a1? And if I do that, would be projection from a2 onto a1 be a1(a1Ta1)-1aT? But what about for a2? Not sure if that's right either. Thanks.
     
  2. jcsd
  3. Feb 23, 2007 #2
    Figured out. misunderstood the problem at first. thanks.
     
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