Quite often the best "explanation" for a sequence is not a low degree polynomial. An example from several days ago was s=: [: p: _1 + 2 ^ i. s1=: 2^i. would be a even shorter example.
----- Original Message ----- From: Kip Murray <[email protected]> Date: Thursday, August 20, 2009 8:09 Subject: Re: [Jprogramming] Takes from a mystery sequence To: Programming forum <[email protected]> > P.S. Well, any data has an exact polynomial fit, so maybe I > should have said > "exact low degree polynomial fit". Maybe what I want is a > verb whose left > argument n requests a fit of degree n or less for the right argument. > > Kip Murray wrote: > > Thank you, Ambrus, I will study your verbs. Of course I > would like the lowest > > degree that fits the data. I'm assuming data that has an > exact polynomial fit. > > > > Kip > > > > Zsbán Ambrus wrote: > >> On Tue, Aug 18, 2009 at 11:27 PM, Kip > Murray<[email protected]> wrote: > >>> Have you seen a polynomial-fitting verb for data such as > iii0 10 and iii1 10 ? > >> Sure, and it's quite simple: > >> > >> se0=: 1 4 7 10 13 > 16 19 22 25 28 > >> se1=: 0 4 20 54 112 200 324 490 704 972 > >> ]p0 =: (%.[:^/~...@#) se0 > >> 1 3 7.97184e_8 _7.964e_8 4.15017e_8 _1.25439e_8 2.27913e_9 > >> _2.45331e_10 1.44069e_11 _3.55401e_13 > >> p0 p. i. 10 > >> 1 4 7 10 13 16 19 22 25 28 > >> ]p1 =: (%.[:^/~...@#) se1 > >> _7.96167e_11 2.1526e_7 3 1 _2.66006e_7 7.83796e_8 _1.39068e_8 > >> 1.46474e_9 _8.43371e_11 2.04392e_12 > >> p1 p. i. 10 > >> _7.96167e_11 4 20 54 112 200 324 490 704 972 > >> NB. or, if you want lower degree polynomyals > >> ]p0d2 =: (%.2^/&i.~#) se0 > >> 1 3 > >> p0d2 p. i. 10 > >> 1 4 7 10 13 16 19 22 25 28 > >> ]p1d4 =: (%.4^/&i.~#) se1 > >> 1.3074e_12 _2.50111e_12 3 1 > >> p1d4 p. i. 10 > >> 1.3074e_12 4 20 54 112 200 324 490 704 972 > >> > >> Ambrus ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
