Re: Fast solution to very small eigenvalue problem

From: Mark Mackey (markm_at_chiark.greenend.org.uk)
Date: 06/25/04 

Date: 25 Jun 2004 11:10:49 +0100 (BST)

In article <avMCc.131446$Gx4.109902@bgtnsc04-news.ops.worldnet.att.net>,
K. Doniger <k.doniger@ieee.org> wrote:
>>
>If this derives from a physical problem, perhaps you can use Rayleigh's
>variational principle.

The problem involves aligning molecules in 3D. The problem reduces down
to constructing a symmetric 4x4 matrix from the atomic coordinates, and
the eigenvector corresponding to the largest eigenvalue of that matrix
is the rotation quaternion giving the best least-squares fit (see
http://www.osc.edu/PET/CCM/skeleton/software/tested/source/qtrfit/qtrfit_theory.html,
with the caveat that the matrix is depicted wrongly: it is actually
symmetric) 

-- 
Mark Mackey 
"The determined Real Programmer can write Fortran programs in any language."
		 - "Real Programmers don't use Pascal"

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