Re: Polynomial fitting routines?

In article <dmibok$jah$1@xxxxxxxxxxxxxxxxxxxxxxx>, Steven G. Kargl wrote:
> In article <hQ1jf.20167$KP1.10251@xxxxxxxxxxxxxxxxxxxxxx>,
> Charles Russell <SPAMworFREEwor@xxxxxxxxxxxxx> writes:
>> Steven G. Kargl wrote:
>>
>>>
>>> I'm looking for an algorithm that will fit a polynomial to
>>> log(x) for 0.25 <= x <= 2 with at least 64-bit precision.
>>
>> A couple of old books deal with this: John F. Hart et al, Computer
>> Approximations, and W. J. Cody and W. Waite, Software Manual for the
>> Elementary Functions. You may need a rational rather than a polynomial
>> approximation. If you google, try "approximation" for your problem
>> rather than "fitting."
>
> Thanks. I'll see if I can find a copy. I pulled out
> a copy of Hildebrand's "Introduction to Numerical Analysis"
> to review the section on developing a minimax polynomial
> approximation. As I paged through the book, I came across
> Section 7.9 on least squares and Chebyshev approximations.
> I actually derived the integrals in Eq. 7.9.15 for my
> problem. Unfortunately, after the first one, the others
> are not easily solved. However, the integrals in 7.9.17
> can be solved, so I have a lead.

I guess this is bordering on stating the obvious; a lot of stuff for
rational approximation is stuffed under the heading "Padé
approximation". This is iirc heavily used in control theory.


--
Janne Blomqvist
.

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