On Sep 19, 5:12 pm, rjf <[email protected]> wrote: > Any program that computes a quadrature by evaluating the integral at > selected points cannot provide > a rigorous error bound. I don't know what a rigorous "error estimate" > is, unless it is an > estimate of what might be a rigorous bound. And thus not rigorous at > all, since the > estimate might be wrong. > That's true, but it is important that automated routines do good error estimation especially for smooth functions. But it is the wrong way to say: Hey I can't do it for every case, so why bother? The example I gave is smooth simple function but causes already troubles.
> A nasty function: f(x) := if member(x,evaluation_point_set) then 0 > else 1. > integrate(f,a,b) should be b-a. The numerical integration program > returns 0. This nasty functions are the reason why I suggested already on trac that is necessary to allow the user to give customized integration points (I can show you much less nasty functions), and for example scipy allows this, and mpmath allows different integration methods. Of course for special points error estimation is hard or even impossible, but if the user do it by him/herself one could assume that he/she knows what it does. ... > RJF > greez, maldun -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
