[cctbxbb] FYI: The Quaternion Characteristic Polynomial method

[Jeffrey Van Voorst]

Greetings,

If you already know about the quaternion characteristic polynomial 
method for a fast closed-form solution of the least squares 
superposition problem, this note is mostly noise.

While in the process of updating links to my project, I noticed the note 
at the bottom of the cctbx sourceforge page 
(http://cctbx.sourceforge.net/).  I like the historical nature 
presented, and I used the historical method to numerically solve quartic 
polynomials in a previous project at Michigan State University that 
ranks relatively large datasets of protein small-molecule binding sites 
(with respect to a given query site). The superposition method I used 
has a closed form and is due to BKP Horn.

Later on (after writing my dissertation), I found that using the 
historical method to numerically solve quartic polynomials is not 
numerically stable or robust.  Fortunately, there is an easy solution, 
and if you are interested in a fast closed-form solution for the least 
squares superposition problem you would do well (in my opinion) to visit 
http://theobald.brandeis.edu/qcp/.

Best regards,

Jeff Van Voorst