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Fri Mar 15 14:30:11 EDT 2013

Normalization: a-symmetric

See also [1].  I'm looking for a simpler, a-symmetric approach where
only one of the coefficients is updated, e.g. c.  Solving for f(c) = 0 in

   f(c) = (c^2 + s^2) - 1

the N-R update is:

   u(c) = c - f(c) / f'(c)
        = c - (c^2 + s^2 - 1) / 2c

        = 1/2 (c + (1-s^2)/c)

This is probably much more precise than the other method, but it uses
a division operator.  Also, it's symmetric in c and s, so if c->0 we
can switch to the s form.

The direct form is probably better.


[1] entry://20130309-182723

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