Solutions of Multivariate Polynomial Systems using Macaulay Resultant Expressions
Finding zeros of algebraic sets is a fundamental problem in aerospace engineering computation. Geometrically, this problem can often be represented by the intersection of multiple conic or quadric surfaces. A common example is GPS trilateration, which is geometrically given by the intersection of three spheres. In this work, Macaulay resultant expressions are used to compute the solutions of a set of multivariate polynomial expressions. Both two- and three-dimensional algebraic sets are considered, and examples of two geometric systems and their solutions are provided.
K. A. Legrand et al., "Solutions of Multivariate Polynomial Systems using Macaulay Resultant Expressions," Proceedings of the 24th AAS/AIAA Space Flight Mechanics Meeting (2014, Santa Fe, NM), vol. 152, pp. 421 - 438, Univelt Inc., Jan 2014.
24th AAS/AIAA Space Flight Mechanics Meeting (2014: Jan. 26-30, Santa Fe, NM)
Mechanical and Aerospace Engineering
Keywords and Phrases
Algebra; Multivariable systems; Space flight; Algebraic sets; Engineering computation; Geometric systems; Macaulay resultant; Multivariate polynomial; Quadric surfaces; Trilateration; Polynomials
International Standard Book Number (ISBN)
International Standard Serial Number (ISSN)
Article - Conference proceedings
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01 Jan 2014