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The secant equation
Let us define a general polynomial of degree 2:

(13.27) 
where
are constant. From the rule for differentiating a
product, it can be verified that:
if and depend on . It therefore
follows from 13.27 (using
) that

(13.28) 
A consequence of 13.28 is that if and
are two given points and if
and
(we simplify the notation
), then

(13.29) 
This is called the ``Secant
Equation''. That is the Hessian matrix maps the differences in
position into differences in gradient.
Frank Vanden Berghen
20040419