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1.2.1 NGF Interpolation
Let us first construct a polynomial of order by using
only points to the right of (and itself).
Written in terms of forward differences, we have
Newton-Gregory Forward interpolation:
where
By
we denote the neglected remainder, stressing its
gross dependence on the step size .
Close analysis would show that the remainder term is actually
where is the position of the maximum of
in the interval
. Putting
we have
EXAMPLE:
Taking in the general NGF formula we obtain
the parabolic approximation
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001