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Kim
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 Posted: Thu Nov 13, 2008 11:07 am Post subject: Formula to number sequence |
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How do I approach finding a formula from a sequence of number pairs ?
I have 17 number pairs from the sequence and I suspect that power>ing
(ie 81^2.4) is used, but no idea to what.
81 1120
82 1800
83 2533
84 3316
85 4151
86 5045
87 5981
88 6979
89 8032
90 9143
91 10323
92 11544
93 12835
94 14189
95 15606
96 17106
97 18637 |
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Kim
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| Posted: Fri Nov 14, 2008 12:48 pm Post subject: Re: Formula to number sequence |
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On Nov 13, 12:07 pm, Kim <kims...@gmail.com> wrote:
[quote]How do I approach finding a formula from a sequence of number pairs ?
I have 17 number pairs from the sequence and I suspect that power>ing
(ie 81^2.4) is used, but no idea to what.
81 1120
82 1800
83 2533
84 3316
85 4151
86 5045
87 5981
88 6979
89 8032
90 9143
91 10323
92 11544
93 12835
94 14189
95 15606
96 17106
97 18637
[/quote]
Is this too hard, too many/much unknown or simply not interesting
(enough) ?
Maybe I posted this request the wrong place, if so please direct me to
the correct place. But I posted here because the description said
"Numerical Analysis" and this is just that. |
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Wolfgang Rave
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| Posted: Fri Nov 14, 2008 12:51 pm Post subject: Re: Formula to number sequence |
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On Nov 13, 12:07 pm, Kim <kims...@gmail.com> wrote:
[quote]How do I approach finding a formula from a sequence of number pairs ?
I have 17 number pairs from the sequence and I suspect that power>ing
(ie 81^2.4) is used, but no idea to what.
81 1120
82 1800
83 2533
84 3316
85 4151
86 5045
87 5981
88 6979
89 8032
90 9143
91 10323
92 11544
93 12835
94 14189
95 15606
96 17106
97 18637
[/quote]
This seems to be a simple parabola. Try f(x) = a*x^2 + b*x + c and
choose 3 pairs of data to find a, b and c. Looks quite trivial. At
first sight I think a = 29, b ~ -4000 and c ~ 140000, something like
that (without detailed calculation). Another approach might be f(x) (x - a)² + b, which uses only a and b and might be even easier to do.
Good luck, Wolfgang. |
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Greg Heath
Guest
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| Posted: Fri Nov 14, 2008 2:00 pm Post subject: Re: Formula to number sequence |
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On Nov 14, 7:51 am, Wolfgang Rave <i...@rave-edv.de> wrote:
[quote]On Nov 13, 12:07 pm, Kim <kims...@gmail.com> wrote:
How do I approach finding a formula from a sequence of number pairs ?
I have 17 number pairs from the sequence and I suspect that power>ing
(ie 81^2.4) is used, but no idea to what.
81 1120
82 1800
83 2533
84 3316
85 4151
86 5045
87 5981
88 6979
89 8032
90 9143
91 10323
92 11544
93 12835
94 14189
95 15606
96 17106
97 18637
This seems to be a simple parabola. Try f(x) = a*x^2 + b*x + c and
choose 3 pairs of data to find a, b and c. Looks quite trivial. At
first sight I think a = 29, b ~ -4000 and c ~ 140000, something like
that (without detailed calculation). Another approach might be f(x) > (x - a)² + b, which uses only a and b and might be even easier to do.
[/quote]
I didn>t plot the data. However, if a polynomial
is indicated, use all of the data and obtain a
set of linear equations in the coefficients.
However, if nonintegral powers are indicated you
might try a polynomial in log(x).
Hope this helps.
Greg |
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nottoo
Guest
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| Posted: Sat Nov 15, 2008 12:48 pm Post subject: Re: Formula to number sequence |
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You might try plotting them in excel, then trying the various curve
fits. You never know, might be a polynomial or exponential or
something.
On Nov 14, 12:07 am, Kim <kims...@gmail.com> wrote:
[quote]How do I approach finding a formula from a sequence of number pairs ?
I have 17 number pairs from the sequence and I suspect that power>ing
(ie 81^2.4) is used, but no idea to what.
81 1120
82 1800
83 2533
84 3316
85 4151
86 5045
87 5981
88 6979
89 8032
90 9143
91 10323
92 11544
93 12835
94 14189
95 15606
96 17106
97 18637[/quote] |
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Raoul Fleckman
Guest
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| Posted: Sat Nov 15, 2008 6:24 pm Post subject: Re: Formula to number sequence |
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On 2008-11-14, Greg Heath <heath@alumni.brown.edu> wrote:
[quote]On Nov 14, 7:51?am, Wolfgang Rave <i...@rave-edv.de> wrote:
On Nov 13, 12:07?pm, Kim <kims...@gmail.com> wrote:
How do I approach finding a formula from a sequence of number pairs ?
I have 17 number pairs from the sequence and I suspect that power>ing
(ie 81^2.4) is used, but no idea to what.
81 ? ? ?1120
82 ? ? ?1800
83 ? ? ?2533
84 ? ? ?3316
85 ? ? ?4151
86 ? ? ?5045
87 ? ? ?5981
88 ? ? ?6979
89 ? ? ?8032
90 ? ? ?9143
91 ? ? ?10323
92 ? ? ?11544
93 ? ? ?12835
94 ? ? ?14189
95 ? ? ?15606
96 ? ? ?17106
97 ? ? ?18637
This seems to be a simple parabola. Try f(x) = a*x^2 + b*x + c and
choose 3 pairs of data to find a, b and c. Looks quite trivial. At
first sight I think a = 29, b ~ -4000 and c ~ 140000, something like
that (without detailed calculation). Another approach might be f(x) =
(x - a)? + b, which uses only a and b and might be even easier to do.
I didn>t plot the data. However, if a polynomial
is indicated, use all of the data and obtain a
set of linear equations in the coefficients.
However, if nonintegral powers are indicated you
might try a polynomial in log(x).
Hope this helps.
Greg
[/quote]
gnuplot>s fit for f(x) = a*x^2 + b*x + c results in:
====================================================
After 10 iterations the fit converged.
final sum of squares of residuals : 5843.91
rel. change during last iteration : -1.29174e-13
degrees of freedom (FIT_NDF) : 14
rms of residuals (FIT_STDFIT) = sqrt(WSSR/ndf) : 20.4309
variance of residuals (reduced chisquare) = WSSR/ndf : 417.422
Final set of parameters Asymptotic Standard Error
======================= ==========================
a = 28.8604 +/- 0.232 (0.804%)
b = -4046.07 +/- 41.32 (1.021%)
c = 139530 +/- 1835 (1.315%)
[shrug]
--
r |
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