(PC-12xx~14xx) qthsh Tanh-Sinh quadrature

[robve]

(04-02-2021 03:16 PM)Albert Chan Wrote:  

https://www.genivia.com/files/qthsh.pdf, page 10 Wrote:mpmath: mp.dps=15, points=53, est.err=1e-14 (incorrect, actual is about 1e-9)

I was unable to produce above result, for ∫(x**3 - 2x*x + x, x = 0 .. 1)

See the number in the table in the article: (53,1E-14#) which is about the same what you found. I neglected to update the title with the correct number. The relative error is about 1E-17~1E-16 to be fair.

The mpmath error estimation is a bit of a mystery to me, given the numbers and the way it is estimated in the code. It seems too high or too low in several cases.

- Rob