Solutions of Multivariate Polynomial Systems using Macaulay Resultant Expressions
Abstract
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.
Recommended Citation
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.
Meeting Name
24th AAS/AIAA Space Flight Mechanics Meeting (2014: Jan. 26-30, Santa Fe, NM)
Department(s)
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)
978-0877036111
International Standard Serial Number (ISSN)
0065-3438
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2014 Univelt Inc., All rights reserved.
Publication Date
01 Jan 2014