Simpson's Rule - Alternative Extended Simpson's Rule

Alternative Extended Simpson's Rule

This is another formulation of a composite Simpson's rule: instead of applying Simpson's rule to disjoint segments of the integral to be approximated, Simpson's rule is applied to overlapping segments, yielding:


\int_a^b f(x) \, dx\approx
\frac{h}{48}\bigg.

Read more about this topic:  Simpson's Rule

Famous quotes containing the words alternative, extended, simpson and/or rule:

    If you have abandoned one faith, do not abandon all faith. There is always an alternative to the faith we lose. Or is it the same faith under another mask?
    Graham Greene (1904–1991)

    I have been accustomed to make excursions to the ponds within ten miles of Concord, but latterly I have extended my excursions to the seashore.
    Henry David Thoreau (1817–1862)

    The man who married Magdalene
    Had not forgiven her.
    God might pardon every sin . . .
    Love is no pardoner.
    —Louis Simpson (b. 1923)

    Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.
    Nelson Goodman (b. 1906)