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1.2.3 ST Interpolation
Let us try to interpolate around employing the central differences
,
etc.
Difficulty:
Central differences of odd order cannot be
evaluated using a given table of function values.
Replace each term of the form
by its central
mean. We find the even order polynomials
Stirling interpolation:
EXAMPLE:
With (or ) we have
In a region symmetric about the Stirling polynomial gives,
for equal orders of error, the ``best'' approximation to the tabulated
function.
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001