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Topic: Weigthened least squares
Replies: 2   Last Post: Jul 3, 2013 5:33 AM

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Torsten Hennig

Posts: 2,419
Registered: 12/6/04
Re: Weigthened least squares
Posted: Jul 3, 2013 4:59 AM
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> Hello,
>
> I have the following Equality:
>
> A^T D A x = A^T D b
>
> where A has many rows, but only five colums
>
> D is a square diagonal matrix (Weights)
>
> b is a column vector
>
> and x is solved for
>
>
> According to my source text, this is the solution of
> a particular weighted least squares problem.
>
> My question, is it possible to express this as an
> overdetermined system, which is solved in the least
> squares sense?
>
> like
>
> D_1 A x = D_2 b
>
> ??


The underlying overdetermined system is given by
sqrt(D)*(A*x-b) = 0

Best wishes
Torsten.



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