Positivity Conditions for Quartic Polynomials

Ulrich, Gary and Watson, Layne T. (1990) Positivity Conditions for Quartic Polynomials. Technical Report TR-90-57, Computer Science, Virginia Polytechnic Institute and State University.

Abstract

Simple necessary and sufficient conditions that a quartic polynomial f(z) be non-negative for z greater than or equal to 0 or a is less than or equal to z and z is less than or equal to b are derived, and illustrated geometrically. The geometry provides considerable insight and suggests various approximations and computational simplifications. The theory is applied to monotone quintic spline interpolations, giving necessary and sufficient conditions and an algorithm for monotone Hermite quintic interpolation.