2017
DOI: 10.1080/00207160.2016.1276572
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Complexity of constructing Dixon resultant matrix

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Cited by 12 publications
(13 citation statements)
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“…A complexity analysis on construction of the Dixon resultant matrix is given in [31,Theorem 3.1] which is of order of O (š‘›! 3 š”Ŗ 4š‘› ) where š”Ŗ is the maximal univariate degree of the polynomials in š¹ in each of its variables.…”
Section: Using the Multivariate Dixon Resultantmentioning
confidence: 99%
“…A complexity analysis on construction of the Dixon resultant matrix is given in [31,Theorem 3.1] which is of order of O (š‘›! 3 š”Ŗ 4š‘› ) where š”Ŗ is the maximal univariate degree of the polynomials in š¹ in each of its variables.…”
Section: Using the Multivariate Dixon Resultantmentioning
confidence: 99%
“…| [Qin, Wu, Tang et al (2017); Grenet, Koiran and Portier (2013)]. Therefore, in each phase of selecting all neighboring points and considering the smallest size of the Dixon matrix, we have a complexity as O(kd 3 n d ).…”
Section: Optimizing Methods For Dixon Matrixmentioning
confidence: 99%
“…However, it is generally known that the entries of the Dixon matrix are more complicated than the entries of other resultant matrices. As a promising scheme, the fast recursive algorithm of the Dixon matrix (FRDixon for short) [11][12][13][14][15][16] can greatly improve the computation efficiency of the Dixon matrix. Recently, its effectiveness has been analyzed in detail and proven by [16].…”
Section: Introductionmentioning
confidence: 99%
“…As a promising scheme, the fast recursive algorithm of the Dixon matrix (FRDixon for short) [11][12][13][14][15][16] can greatly improve the computation efficiency of the Dixon matrix. Recently, its effectiveness has been analyzed in detail and proven by [16]. Nevertheless, the size of the Dixon matrix and computational complexity by FRDixon explode exponentially as the number of variables increases.…”
Section: Introductionmentioning
confidence: 99%