Still, it doesn't hurt to check with differences. Maybe it IS a polynomial! And a polynomial may be a good practical fit for a take of the sequence.
Roger Hui wrote: > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
