Acron RPN announces v3.0 BETA

[Paul Dale]

I'm with Dieter, pick a better algorithm. For example, a two point Gaussian quadrature is exact for cubic polynomials which includes the x² example. Romberg is an easy choice and is adaptive. Also interesting are the Gauss–Kronrod quadratures, although they will need to be made adaptive.

As for trapezoidal vs rectangular, it depends how you define the latter. Using the function value at the middle of the rectangles for the height (rather than at the left or right edge) produces an error term twice that of the trapezoidal for one less function evaluation. Using either edge to define the rectangles is worse. Wikipedia illustrates this okay. Computationally, they are about the same (but trapezoidal requires one more function evaluation).


Pauli