Complexity of constructing Dixon resultant matrix

Dixon resultant is a fundamental tool of elimination theory in the study and practice of algebraic geometry. It has provided the efficient and practical solutions to some benchmark problems in a variety of application domains, such as automated reasoning, automatic control, and solid modelling. The...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 94; no. 10; pp. 2074 - 2088
Main Authors: Qin, Xiaolin, Wu, Dingxiong, Tang, Lin, Ji, Zhenyi
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.10.2017
Taylor & Francis Ltd
Subjects:
Algebra
Automated reasoning
Automatic control
Bivariate analysis
Complexity
Computation
computational complexity
Dixon resultant matrix
elimination theory
Matrices (mathematics)
Parallel processing
Polynomial system solving
Polynomials
recursive algorithm
Solid modelling
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:Dixon resultant is a fundamental tool of elimination theory in the study and practice of algebraic geometry. It has provided the efficient and practical solutions to some benchmark problems in a variety of application domains, such as automated reasoning, automatic control, and solid modelling. The major task of solutions is to construct the Dixon resultant matrix, the entries of which are more complicated than the entries of other resultant matrices. An existing extended recurrence formula can construct the Dixon resultant matrix fast. In this paper, we present a detailed analysis of the computational complexity of the recurrence formula for the general multivariate setting. Parallel computation can be applied to speed up the recursive procedure. Furthermore, we also generalize the computational complexity of three bivariate polynomials to the general multivariate case by using the construction of standard Dixon resultant matrix. Some experimental results are demonstrated by a range of nontrivial examples.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2016.1276572