Often it is not a good idea evaluate numerical derivatives with a too small step size, due to it amplifies the error on incremental quotients. It is better to evaluate it for several bigger values and then extrapolate the limit.
Best,
M
2014-06-12 13:25 GMT-03:00 epquinn@pks.mpg.de:
I am taking numerical derivatives (acknowledging that it's not generally the best idea), and the data exhibits some peaks that look spurious. When I try to resolve them the errors in the values for the ground state energy become significant. My idea was that if I could control the accuracy of the ground state energy values I could determine whether the peaks are indeed there.
Related to the 10 digits of accuracy, the error becomes very noticeable in the second derivative of the data already for a step size of 0.001.
Best, Eoin
sparsediag should always give you at least 10 digits of accuracy. What inaccuracy are you talking about?
On 12 Jun 2014, at 00:09, epquinn@pks.mpg.de wrote:
Thanks for the response. Two or three decimal places more should be enough to allow me clearly see the features I am looking at. The problem is that at the moment the inaccuracy is washing them out.
What accuracy are you aiming for?
On Jun 11, 2014, at 6:42, epquinn@pks.mpg.de wrote:
Greetings,
I am wondering if it is possible to increase the accuracy of sparsediag, for example for the result it gives for the lowest eigenvalue. There does not appear to be a suitable input parameter. My understanding is that increasing accuracy comes at a computational cost, and I need to tweak the balance further to the side of accuracy.
With best regards, Eoin