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

[robve]

(04-17-2021 11:45 PM)Albert Chan Wrote:  There may be a flaw with this ...

With sign checking method, both will suggest optimal d ~ 700.

Not so fast. In your example the left side's magnitude f(a+d/v)/v is larger than f(a+d*v)*v which means that the sign changes for a different reason. In my test this shows that d should be small (because the test also takes the magnitudes of the difference into account). So your example is not a counter example of my earlier post on why this might work.

Furthermore, as you will notice, the sign change is not always the exact place for an optimal d, but close. The magnitude change is a critical indicator (and more reliable) in the neighborhood of the sign change. So far it works every time.

I was surprised that when I discovered this that for all integrals of the 208 the sign change suggests there is a solid predictor based on this that can be perfected with some tweaking.

- Rob