The tanh-sinh quadrature

[emece67]

(03-08-2017 02:42 AM)Paul Dale Wrote:  This method looks interesting but I'm not convinced it should be part of the standard 34S firmware.

I originally used a Gauss-Kronrod quadrature in the 34S. As with all quadrature methods, it didn't always work and it wasn't adaptive but it was pretty fast. Enough people pointed out specific failure cases and wanted Romberg that I changed the method over. Rapidly oscillating functions and some exponential were bad from memory.

Still, publish the code please,

- Pauli

In fact this is an adaptive quadrature. The number of abscissas is doubled on each iteration and the method stops when the computed integral changes by less than the needed precision. The difference with the previous Gauss-Kronrod method on the wp34s is, I think, that here the abscissas and weights are computed on the fly, so you are not constrained to a given number of precomputed samples.

In any case, my implementation of this method for the wp34s does stop the algorithm when the needed precision has been reached or after a number of functions evaluations has been reached. Relaxing this criteria will give better results for such problematic functions. I'll test it.

Regards.