Title

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.

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)

9780877036111

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.

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