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Re: What is the meaning of this pattern of polynomial coefficients?
From: |
Robert A. Macy |
Subject: |
Re: What is the meaning of this pattern of polynomial coefficients? |
Date: |
Mon, 31 Jan 2005 19:29:18 -0800 |
Group,
Have more to add. After judiciously scaling the ordinate,
to some interim value, making the ordinate go between 0.5
and up to around 2; then the high and low coefficient
magnitudes become EXACT mirror images of themselves.
For example, pretend the minus sign is really a 180 phase
shift, then the polynomial always takes the form of
for n being odd...
A*x^n - B*x^(n-1) + C*x$(n-2) ... - C*x^2 + B*x - A
and for n being even...
A*x^n - B*x^(n-1) + C*x$(n-2) ... + C*x^2 - B*x + A
for 2 < n < 17
plus one more feature...
The center values dominate with the center
coefficient located at round(n/2)+1 being the maximum value
If I plot the log of the magnitudes of the coefficients, it
looks exactly like an inverted parabola with the peak in
the center index.
The original data is derived from a physical observation
and I did not expect to see such symmetry.
Is there a better curve fit than a polynomial for this
family of curves?
- Robert -
On Mon, 31 Jan 2005 11:43:31 -0800
"Robert A. Macy" <address@hidden> wrote:
> Group,
>
> Ive got a matrix of complex values.
>
> Each row relates to one variable.
>
> Along each row relates to an ordinate (vector).
>
> After doing a polynomial fit for each row whether 2, 3,
> 4,
> 5,
are used for the number of coefficients; the
> characteristics of those coefficients look almost
> identical! Except for every other one is shifted in
> phase
> by 180 degrees and their magnitude is different, but
> their
> shape in the complex plane is almost identical.
>
> What is the significance of this?
>
> - Robert
>
>
>
>
>
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