Re: How to find a formula from a list of numbers

Article View: aus.mathematics

Article #38

#38

From: Barb Knox
Date: Sun, 04 Oct 2009 23:40

52 lines
2846 bytes

In article <mq6dnbOR7_Sjv1TXnZ2dnUVZ_r6dnZ2d@westnet.com.au>,
 Adam Nielsen <a.nielsen@remove.this.shikadi.net> wrote:

> > The simple divide and subtract will also keep the code nice and fast.  
> > However
> > I'm not so sure one of the other rails will be that easy:
> > 
> >   A  |  B'
> > -----+-----
> >  0   | 0
> >  1   | 0.1
> >  4   | 0.4
> >  8   | 0.9
> >  16  | 1.9
> >  32  | 3.8
> >  48  | 5.7
> >  64  | 7.6
> >  96  | 11.4
> >  128 | 15.2
> >  160 | 19.1
> >  192 | 22.9
> >  208 | 24.8
> >  224 | 26.7
> >  255 | 30.4
> 
> Oh having said that, I think this might work:
> 
>   B' = A/10 + A/52
> 
> Not sure quite how their rounding works, so let me know if you have any 
> better
> ideas!

Note that for A >= 16, doubling A also doubles B'.
The best fit is
    B' = A/16 * 1.91, truncated to 1 decimal place.

1.91/16 = 0.119375,
and your rational approximation for that is 
    1/10 + 1/52 = 31/260 = 0.1192307

Note that there are closer rational approximations, but any one that 
provides the correct B' values to 1 decimal place is close enough.

-- 
---------------------------
|  BBB                b    \     Barbara at LivingHistory stop co stop uk
|  B  B   aa     rrr  b     |
|  BBB   a  a   r     bbb   |    Quidquid latine dictum sit,
|  B  B  a  a   r     b  b  |    altum viditur.
|  BBB    aa a  r     bbb   |   
-----------------------------

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From: Barb Knox <see@sig.below>
Newsgroups: aus.mathematics
Subject: Re: How to find a formula from a list of numbers
Date: Mon, 05 Oct 2009 12:40:12 +1300
Organization: I'm not unemployed; I'm a consultant
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