Re: Polynomial fitting routines?

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.

--
Steve
http://troutmask.apl.washington.edu/~kargl/
.

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