Need references for MiniMax fitting

[Namir]

Hi All,

Valentin Albillo has published on his web site an HP-71B BASIC program that calculates the minimax coefficients of polynomials that pass through a discrete set of data. As I find myself interested in the algorithms used to evaluate basic transcendental functions, Valentin's approach comes across as very practical and useful. He provides a minimax polynomial that is very easy to evaluate.

I would like very much to obtain references for the algorithms behind the minimax polynomial fit. Links to web sitss or references to books are most appreciated.

Namir

Edited: 6 Sept 2006, 9:35 p.m.

[Valentin Albillo]

Hi, Namir:

Thanks a lot for your kind remarks and your interest in my HP-71B Minimax Polynomial Fit program (freely downloadable in PDF format from my HP calc web site).

These references might prove useful to you as a start:

• Ref. 1 (PDF document)

• Ref. 2 (PDF document)

• Ref. 3 (PDF document)

• Ref. 4 (Web site, theory and plenty of useful examples, with graphics)
  

Best regards from V.

[Namir]

Excellent Valentin. Many many thanks for these references. I have tried coding (using Excel VBA so far) different methods to evaluate e^x, the basic trig functions and their inverses. The minimax polyomial that you showed in a previous post is the most practical for a handheld calculator (as an exercise of course). I have used the approximation by summing the products of constants coefficients with shifted Chebyshev polynomials. While they work ok in VBA (or any other high-level langauge), they are no practical to implement on a vintage programmable calculator like the HP-67.

Again, thanks for the references.

Namir