Re: Polynomial fitting routines?

On 2005-11-29 15:20:57 -0400, Charles Russell <SPAMworFREEwor@xxxxxxxxxxxxx> said:

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." 

Another golden oldie on approximation was by Hastings. He showed
how to use the the properties of the functions to choose the
form of the approximation which allowed for lowering the order.

Cody and Kuki did the math library for IBM 360s so there may
so citations of interest.

HASTINGS, C., JR. 1955.
APPROXIMATIONS FOR DIGITAL COMPUTERS.
PRINCETON, NJ: PRINCETON UNIVERSITY PRESS.

.

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