Bounds for resultants of univariate and bivariate polynomials

DOI10.1016/j.laa.2009.08.012zbMath1220.13021OpenAlexW1979424209MaRDI QIDQ848582

Alexander Lifshitz, Yuval Bistritz

Publication date: 4 March 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.08.012

zbMATH Keywords

Sylvester matrixresultantBezoutianHadamard bound

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Matrices, determinants in number theory (11C20) Solving polynomial systems; resultants (13P15)

Related Items (13)

Matrix algebraic properties of the Fisher information matrix of stationary processes ⋮ Number of common roots and resultant of two tropical univariate polynomials ⋮ A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm ⋮ Higher-dimensional sieving for the number field sieve algorithms ⋮ Solving discrete logarithms on a 170-bit MNT curve by pairing reduction ⋮ Codes correcting restricted errors ⋮ Computing discrete logarithms in \(\mathbb F_{p^6}\) ⋮ Computing Generator in Cyclotomic Integer Rings ⋮ Efficient \(q\)-integer linear decomposition of multivariate polynomials ⋮ Fraction-free computation of the unit-circle resultant with any singularity profile ⋮ Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case ⋮ Asymptotic complexities of discrete logarithm algorithms in pairing-relevant finite fields ⋮ An algorithmic approach to Chevalley’s Theorem on images of rational morphisms between affine varieties

Cites Work

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• Computational aspects of deciding if all roots of a polynomial lie within the unit circle
• Generalized Bezoutians and families of efficient zero-location procedures
• Zero location of polynomials with respect to the unit-circle unhampered by nonessential singularities
• On testing stability of 2-D discrete systems by a finite collection of 1-D stability tests
• Subresultants and Reduced Polynomial Remainder Sequences
• On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
• On Euclid's Algorithm and the Theory of Subresultants
• Algorithms in real algebraic geometry

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