FindFit

*To*: mathgroup at smc.vnet.net*Subject*: [mg62540] FindFit*From*: Montgrimpulo <dto_mba at skynet.be>*Date*: Sun, 27 Nov 2005 02:40:47 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

t={{1,1},{2,1},{3,2},{4,2},{5,4},{6,2},{7,6},{8,4},{9,6},{10,4},{11,10}} f=a+b*x+c*x^2 FindFit[t, f, {a, b, c}, {x}] Out[] {a -> 0.969697, b -> 0.108392, c -> 0.0477855} So far so good. Now, I want to use a different metric in FindFit. However, I'm in doubt if my use of the option "NormFunction" in FindFit is correct. nf[x_] := Max[Abs[x]] FindFit[t, f, {a, b, c}, {x}, NormFunction -> nf] Out[] "The model a+b*x+c*x^2 is linear in the parameters {a, b, c}, but a nonlinear method or non-Euclidean norm was specified, so nonlinear methods will be used. " Out[] The line search decreased the step size to within tolerance specified by \AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease \in the norm of the residual. You may need more than MachinePrecision digits \of working precision to meet these tolerances. Out []{a -> 0.988004, b -> 0.890595, c -> -0.0325868} If I use NMinimize instead, I get with d := t[[All, 2]] - Table[(f /. x -> t[[i, 1]]), {i, 1, Length[t]}] and NMinimize[Max[Abs[d]],{a,b,c}] Out [] {2.42413, {a -> 0.470545, b -> 0.089553, c -> 0.0505806}} as a result. As the preparatory work to use FindFit is less than for NMinimize and as NMinimize is slowes down drastically with increasing number of points (also for NelderMead), I would like to get some hints to improve the result from FindFit. Working with a higher MachinePrecision did not lead to any improvements. Best, Montgrimpulo