Re: Slow Gradient Method.

From: Nick Holford <n.holford@auckland.ac.nz> Subject: Re: Slow Gradient Method. Date: Thu, 31 May 2001 20:12:19 +1200 Niclas, Thank you for your hardly remembered viewpoint :-) Your historical perspective of the evolution of NONMEM IV to NONMEM V is certainly of interest. Given the pedantic nature of the NONMEM Project Group documentation it seems quite reasonable to extrapolate that the SLOW (undocumented) and the NUMERICAL (documented) options do not have identical meanings. But I am not clear why you think a numerical derivative might be quicker than an analytical derivative. Typical numerical derivatives are (f(t+dt) - f(t))/dt while analytical derivatives are f'(t) so unless f'(t) involves at least twice as much computation as f(t) plus the notoriously computationally expensive division by dt it seems that an analytical derivative would usually be faster than a numerical derivative. There are cases I believe when no convenient analytical derivative exists and then of course one must use numerical derivatives. I found that the use of numerical derivatives in MKMODEL seemed to give reasonable results without having to resort to the labour of obtaining analytical derivatives so in terms of the end result I am not sure if there is any real world difference when numerical vs analytical derivatives are used for the purposes of parameter estimation (assuming the analytical derivative is conveniently available). I have copied this message to those directly responsible (Stuart Beal and Alison Boeckmann) to see if they can throw some light on what distinguishes SLOW from NUMERICAL. Nick -- Nick Holford, Divn Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556 http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm