Introducing Polyterms

[Namir]

Hi All,

I have posted a 6-page report on the main page of my website titled Polyterms. The pdf file you download is my way to formalize polyterms as non-othogonal quasi-polynomials used maimly in curve fitting. Polyterms challenge regular polynomials in performing curve fitting between two or more variables. The report explains how I gradually came into devising and using polyterms. It was a journey that spanned many years.

Since 2004, I have been attending annual HHC conferences. A question that was frequently asked is “If mathematicians like Newton, Gauss, and Euler had programmable calculators how would numerical analysis algorithms look like today?” Funny, that no one asked about the effects if these same mathematicians had today’s laptops! I have expressed my opinion in these meetings that the legacy numerical analysis algorithms were influenced by the computing resources available to the legacy mathematicians. My guess, is that these mathematicians hired educated people who could reliably do long calculations by hand—not to mention the painful task of rechecking these calculations! I regard the Gaussian Quadrature and linear regression as examples of algorithms that pushed hand calculations to the limit. Even doing linear regression using slide rules or four function calculators, in the seventies, was a real chore! The report is my attempt to give an answer of how computer power can offer resources for more advanced curve fitting using quasi-polynomials.

Polyterms combine optimization and curve fitting to yield the models that fit calculated or observed data. Polyterms solve true nonlinear curve fitting models. You can think of polyterms, in object-oriented nuances, as a child class of polynomials.

I hope you enjoy reading the 6-page report that discusses the various nuances that are part of polytrems. I hope that the term polyterms takes it rightfull place in curve fitting.

Namir