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Question: speed up calculation using the interpolant option of `dsolve/numeric`

Question:speed up calculation using the interpolant option of `dsolve/numeric`

jakubi 1379 Maple
August 22 2005
1
Looking for faster ways to make chi^2 nonlinear fit calculations, for functions involving integrals, I have compared timings of calculation of chi^2 at a pair of sample points evaluating the integrals by three numerical methods. In the attached worksheet they are called as follows: 1. chin, using evalf(Int(...)) 2. chin2, using the interpolant option (`dsolve/numeric`(sys, range=...)) 3. chin3, using evalf(Int(...,method=_d01ajc)) I have obtained timings with Maple 9.5 using first a Celeron 333 MHz under RH7.1 and then a P4 1.8 GHz under Win XP. My expectation was that the method of the interpolant function were the fastest of the three, as it is evaluated once for all the data points at a given point of the parameter space, while the integrals are to be computed for each data point. However, the timings that I have obtained with the interpolant function method are worst by a factor 5 at least. So, it seems that something in my setup ruins the efficiency. As I am looking to make these calculations for larger data sets, I would expect that the time of the calculation grow fast with the number of data points for evalf@Int methods, while use of an interpolant function should produce a much better scaling. So, could you tell me how to improve the speed of my setup? Regards, Alejandro
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