[Algorithms] Gram-Schmidt orthonormalization

[Pete T. <pet...@sh...>]

I was wondering if anyone has any opinions on using the Gram-Schmidt
algorithm for orthonormalizing a matrix?  The alternative is to simply
normalize the At vector, Right = Up * At, normalize Right, Up = At * Right,
normalize Up (where * means cross product).  I'm sure there's a name for
this algorithm, but I don't know what it is  ;)

The reason I ask is because the latter algorithm seems to cause the matrix
to "drift" after a while after constant re-orthonormalizing.
Performance-wise, both algorithms seem pretty close (the GS algo seems to
have a couple more adds, though).  Is the GS algo accurate/stable?  What's a
good reason for using it? (aside from being extensible into any N-sized
matrices)

Regards,
-Pete