Numerical integration methods

07312022, 04:59 PM
Post: #23




RE: Numerical integration methods
(07242022 08:55 PM)Wes Loewer Wrote: (Note: It's possible that I am mistranslating "ordre". What the paper called "ordre 30" seems to be "degree 29" (ie, 30 terms), but I could be wrong about this. Francophones, please correct me if I am mistaken.)"order" may mean max degree of polynomial where the method is exact, or the exponent in the step of the error, up to the author choice... Quote:Since the 15node GaussKronrod is exact up to degree 22 and the Prime's method is exact up to degree 29, it would seem that the Prime's method is a bit better with only a small added overhead. A slightly more accurate calculation per iteration could occasionally reduce the need for further recursion. It would be interesting to do some comparisons of these two methods with some wellbehaved functions as well as more "temperamental" ones.Yes, it is important not to reevaluate the function for efficiency reasons. The idea is to estimate the error of the order 30 method in h^30 by err1*(err1/err2)^2 where err1=abs(i30i14) is in h^14 and err2=abs(i30i6) in h^6 

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