On Mon, Jan 24, 2011 at 10:58 PM, Dima Pasechnik <dimp...@gmail.com> wrote: > > > On Jan 12, 2:09 pm, mhampton <hampto...@gmail.com> wrote: >> It is a Riemann sum with a non-constant width. > trapezoid rule is what you get if you take the average of the left- > point and the right-point ones. > (for an obvious geometric reason) > > I don't see why width is relevant here.
A Riemann sum is a sum of areas of rectangles (equivalently, a weighted sum of evaluations). The trapezoid rule is equivalent to taking rectangles of half the width, alternating taking the left and right endpoints as the heights. (Or, again equivalently, letting all the "middle" rectangles be twice the width of the two side ones.) >> The usual definition >> allows that as long as the widths of each interval have a limit of >> zero. >> >> -Marshall >> >> On Jan 11, 9:51 pm, Jason Grout <jason-s...@creativetrax.com> wrote: >> >> >> >> > On 1/11/11 6:06 PM,GaganSekhon wrote: >> >> > > Currently, both riemann_sum and riemann_sum_integral_approximation >> > > does not support trapezoid mode. But instead there are separate >> > > function which computes these for trapezoid mode . >> >> > > I am added this mode to both riemann_sum and >> > > riemann_sum_integral_approximation and wanted to take a vote on how >> > > many people think trapezoid function should stay, should be deprecated >> > > or completely deleted >> >> > At first, my vote was to deprecate, then delete the function. However, >> > I think some people might argue that a trapezoid function was not a >> > riemann sum since it is not of the form (width)*(f(point)) like the >> > left, right, and midpoint sums. So maybe a new function that absorbs >> > all of these called approximate_integral or something is in order? >> >> > Jason > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
