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Abstract: Sparse elimination exploits the structure of a set of multivariate polynomials by measuring complexity in terms of Newton polytopes. We examine polynomial systems that generate 0-dimensional ideals: a generic monomial basis for the coordinate ring of such a system is defined from a mixed subdivision. We offer a simple proof of this known fact and relate the computation of a monomial basis to the calculation of Mixed Volume. (Update)
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BibTeX entry: (Update)
Emi96 I.Z. Emiris. On the complexity of sparse elimination. J. Complexity, 12:134166, 1996. http://citeseer.ist.psu.edu/emiris96complexity.html More
@article{ emiris96complexity,
author = "Ioannis Z. Emiris",
title = "On the Complexity of Sparse Elimination",
journal = "Journal of Complexity",
volume = "12",
number = "2",
pages = "134--166",
year = "1996",
url = "citeseer.ist.psu.edu/emiris96complexity.html" }
Citations (may not include all citations):448 A New Polynomial-Time Algorithm for Linear Programming (context) - Karmarkar - 1984
308 Matrix multiplication via arithmetic progressions (context) - Coppersmith, Winograd - 1990
290 The Complexity of Robot Motion Planning (context) - Canny - 1988
144 Convex Bodies: The Brunn-Minkowski Theory (context) - Schneider - 1993
69 A polyhedral method for solving sparse polynomial systems (context) - Huber, Sturmfels - 1992
59 Homotopies Exploiting Newton Polytopes for Solving Sparse Po.. (context) - Verschelde, Verlinden et al. - 1994
50 An Elimination Algorithm for the Computation of all Zeros of.. (context) - Auzinger, Stetter - 1988
48 The Number of Roots of a System of Equations (context) - Bernstein - 1975
43 Newton Polyhedra and the Genus of Complete Intersections (context) - Khovanskii - 1978
34 An Efficient Algorithm for the Sparse Mixed Resultant - Canny, Emiris - 1993
34 Multigraded Resultants of Sylvester Type (context) - Sturmfels, Zelevinsky - 1994
32 Product Formulas for Resultants and Chow Forms (context) - Pedersen, Sturmfels - 1993
31 Efficient Incremental Algorithms for the Sparse Resultant an.. - Emiris, Canny - 1994
25 A Convex Geometric Approach to Counting the Roots of a Polyn.. (context) - Rojas - 1993
24 Multivariate polynomial equations with multiple zeros solved.. (context) - Moller, Stetter - 1994
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