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Ellipsoid algebra: converting forms

  1. Aug 8, 2011 #1
    I have a matrix D (it happens to be in R^(nxm) where n>>m, but I don't think that is relevant at this point). I also have a vector t in R^n.

    I am interested in rewriting the set

    {x | (Dx-t)'(Dx-t) <= c} in standard ellipsoid form: --> {x | (x-z)'E(x-z)<=b} where E is an mxm positive semi definite matrix. So, I'd like to write z, E and b in terms of D, t, and c.

    Is there an algebraic way to do this?

    (The application area is radiation therapy, D represents the so-called dose-influence matrix.)
     
  2. jcsd
  3. Aug 8, 2011 #2

    I like Serena

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    Last edited by a moderator: Apr 26, 2017
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