Re: [Gretl-devel] fdjac precision question

Dear Riccardo, My simple script uses exactly Richardson extrapolation but it uses a simplistic method for defining the step. 3 digits better is by far too large. Clearly, fdjac uses a more advanced way to find h. It looks, as if it has a buglet inside. I'm making a wrapper for quadtable to do easy integration with hansl, and my simplistic sfd2* works systematically better, while it should not to. Oleh *) fd from fdjac 29 грудня 2015, 00:49:01, від "Riccardo (Jack) Lucchetti" < r.lucchetti(a)univpm.it >: On Tue, 29 Dec 2015, oleg_komashko(a)ukr.net wrote: In general, numerical differentiation should never be expected to be accurate to more than a few decimal digits, for the combined effect of the inherent imprecision of machine precision and discrete (as opposed to _truly_ infinitesimal) differentiation. Run this script and you'll see what I mean: <hansl> set echo off set messages off clear set fdjac_quality 0 loop for (x=-1; x<1; x+=2/13) matrix a = {x} printf "x = %5.2f, precision = %d\n", a, \ floor(-log10(abs(1-fdjac(a, sin(a))/cos(x)))) endloop set fdjac_quality 1 loop for (x=-1; x<1; x+=2/13) matrix a = {x} printf "x = %5.2f, precision = %d\n", a, \ floor(-log10(abs(1-fdjac(a, sin(a))/cos(x)))) endloop set fdjac_quality 2 loop for (x=-1; x<1; x+=2/13) matrix a = {x} printf "x = %5.2f, precision = %d\n", a, \ floor(-log10(abs(1-fdjac(a, sin(a))/cos(x)))) endloop </hansl> That said, I would have expected Richardson extrapolation to fare somewhat better in this case. I'll investigate. ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti ------------------------------------------------------- _______________________________________________ Gretl-devel mailing list Gretl-devel(a)lists.wfu.edu http://lists.wfu.edu/mailman/listinfo/gretl-devel