NDLI: The mechanization of multires algorithm and computation of mixed volume using mixed subdivision for sparse resultants

Content Provider	IEEE Xplore Digital Library
Author	Ahmad, Shamsatun Nahar Aris, Nor'aini Kanafiah, Siti Farah Haryatie bt Mohd
Copyright Year	2010
Description	Author affiliation: Department of Mathematics, Faculty of Sciences, Universiti Teknologi Malaysia, Johor, Malaysia (Aris, Nor'aini) \|\| Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Johor, Malaysia (Ahmad, Shamsatun Nahar; Kanafiah, Siti Farah Haryatie bt Mohd)
Abstract	The method of finding the solutions of a system of non-linear polynomial equations has received a lot of attention since ancient times. Recent active ongoing research related to solving such equations is on the construction and implementations of the method of sparse resultant. The aim of this study is to investigate on the mechanization of the multires algorithm for computing sparse resultant matrix. All the input polynomials are of type over-constrained systems. The basic fact about the number of roots of a polynomial system is given by the mixed volume of the Minkowski sum of convex polytopes. The computation of the mixed volume of a given polynomial system using subdivision and volumes of mixed cells is demonstrated. Maple multires package is used to observe about the size of the sparse resultant matrices for some polynomial systems. The results on mixed volume are compared with the respective results on the size of the resultant matrix.
Starting Page	74
Ending Page	79
File Size	403299
Page Count	6
File Format	PDF
ISBN	9781424489879
e-ISBN	9781424489862
DOI	10.1109/CSSR.2010.5773883
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-12-05
Publisher Place	Malaysia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Algorithm design and analysis Computer science Geometry Multires Polynomial Systems Sparse Resultant Polynomials Mixed Volume Subdivision Sparse matrices Mathematical model
Content Type	Text
Resource Type	Article

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