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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
2004-04-19