Strategies for Manipulating
Errors in Newton
Use of High Order Newton Cotes
One could also generate a formula in terms of the same function values
by using the Newton-Cotes formula appropriate to
This gains an extra derivative in error just like Simpson, and error is
is some known number.
In practice, this is not often used because
(a) the implied interpolation of
over a wide range by a high order polynomial can produce disastrous results when
not polynomial (e.g., has similarities in its value
On the other hand, local interpolation by
by a low order polynomial (used in (NI.9)) is much safer;
(b) it is much easier to estimate error in iterated Simpson of equation (NI.9) as we will describe in Section NI.2.
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