Re: OTTI36X Algorithms Message #31 Posted by robert rozee on 1 Sept 2013, 7:38 p.m., in response to message #30 by Bunuel66
you might well be right about the base thing  i was writing at around 3am in the morning here and not 100% awake. btw, what is the exact (symbolic) integral of frac(x), i've tried asking wolfram alpha but just get an animated 'game of life' graphic that goes on forever no matter what i type in (even "2+7")
i would agree with everyone that any numeric integration method will have flaws, and at times will produce erroneous results. the algorithms generally assume they are working with a continuous function, and when presented with a discontinuity struggle.
splitting the problem down the middle:
(1) can anyone find a continuous function that [insert your favourite calculator model here] fails to be able to integrate numerically?
(2) can anyone think of a method for an algorithm to (generically) spot a discontinuity and modify its behaviour to work around it successfully in all/most cases?
and, one more question: is there an expansion of frac(x) that can be expressed in basic operators (+/*) as is the case with all other regular functions?
