Positivity Conditions for Quartic Polynomials

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TR Number
TR-90-57
Date
1990
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Department of Computer Science, Virginia Polytechnic Institute & 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.

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