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## RE: polyfit questions

 From: Frank Palazzolo Subject: RE: polyfit questions Date: Wed, 26 Jul 2006 15:16:32 -0400

```Ok, why are you using f = x .* polyval(...) instead of f = polyval(...)?

I tried doing this problem 2 ways myself, but the success of the
least-squares fit to the inverse seems very dependant on the actual
polynomial "a" used.  Can you give us an "a" vector which you believe has an
inverse in that form?

Thanks,
Frank

-----Original Message-----
On Behalf Of Georg P. Israel
Sent: Tuesday, July 25, 2006 11:37 AM
Subject: polyfit questions

Dear Octave users,

it seems that polyfit does not work for me.
This is not a software issue, but it seems that I overlook some mathematical
issues.

I do have a function of the form of a polynome:

f(x)= a0+a1*x^1+...+a6*x^6

The function gets called with x:= X^2
Hence, the actual function is of the order of 13 with all odd elements zero.

I like to find the inverse function to this function such that:

g(f(x)) = x

g(y) should be notated in the same form as f(x).
If I try to do this with a normal polynome where x:=X then the fitting works
fine. But when I try to do the same with x:=X^2 then this stuff fails
misserably. This means, the resulting approximated polynome is very much
different form the original.

Do I overlook something??

To be more specific:

x = [0:1:215];
f(x) = x .* polyval(a,x.^2);

now, I tried to find the g(y) that has the same form of a polynome as
f(x) but approximates the inverse of this function.

If I define f(x) = x .* polyval(a,x); and it's inverse similar then all
works fine. But if I use a power of two then all fails.

Has anybody an idea how to define this ???

Georg P. Israel
<info at CMOSVision.com>

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