A General Solver Based on Sparse Resultants

Autor:	Emiris, Ioannis Z.
Rok vydání:	2012
Předmět:	Computer Science - Symbolic Computation Computer Science - Numerical Analysis Mathematics - Commutative Algebra 13P15 Solving polynomial systems resultants (Primary) 68W30 Symbolic computation and algebraic computation (secondary) I.1 F.2.1 G.4
Druh dokumentu:	Working Paper
Popis:	Sparse (or toric) elimination exploits the structure of polynomials by measuring their complexity in terms of Newton polytopes instead of total degree. The sparse, or Newton, resultant generalizes the classical homogeneous resultant and its degree is a function of the mixed volumes of the Newton polytopes. We sketch the sparse resultant constructions of Canny and Emiris and show how they reduce the problem of root-finding to an eigenproblem. A novel method for achieving this reduction is presented which does not increase the dimension of the problem. Together with an implementation of the sparse resultant construction, it provides a general solver for polynomial systems. We discuss the overall implementation and illustrate its use by applying it to concrete problems from vision, robotics and structural biology. The high efficiency and accuracy of the solutions suggest that sparse elimination may be the method of choice for systems of moderate size. Comment: 20 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1201.5810 Zobrazit plný text záznamu View this record from Arxiv