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Let's look at the
to
mapping,
on the unit circle, where
and
:
or
In general, the trapezoid rule is a second-order accurate
approximation to a derivative, in the limit of small
(i.e., near
dc). Here, it is third-order accurate along the unit circle at dc.
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Download DigitizingNewton.pdf
Download DigitizingNewton_2up.pdf
Download DigitizingNewton_4up.pdf