Engineering >> Computer Science & Engineering

Analysis of Polynomials Via Newton's Method

by Kyle Hemsley


Submitted : Fall 2014

In computing, mathematical operators such as √, irrational numbers such as π, and trigonometric functions such as sine and cosine are expressed on a low level via linear approximation. Even if a programmer’s code does not use linear approximation, the code libraries it is built upon do. This is because CPU instructions are in the form of basic arithmetic, and native interpretation of irrational numbers and functions involving curvature is impossible.

This project consists of an implementation of Newton’s Method of linear approximation for the analysis of a certain third-order polynomial  written in the C programming language. Using Newton’s Method we can find the approximate roots of the function, its derivative, and its second derivative. This expands upon the originally suggested project by describing minima, maxima, inflection points, and concavity.

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Advisors :
Kanakadurga Nallamshetty, Mathematics and Statistics
Jonathan Burns, Mathematics and Statistics
Ralph Tindell, Computer Science & Engineering
Suggested By :
Ralph Tindell