Toward the best algorithm for approximate GCD of univariate polynomials

DOI10.1016/j.jsc.2019.08.004zbMath1475.13050OpenAlexW3036726925MaRDI QIDQ1994881

Kosaku Nagasaka

Publication date: 18 February 2021

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2019.08.004

zbMATH Keywords

Sylvester matrixQR factorizationapproximate polynomial GCDrank structured matrixsubresultant matrixsymbolic-numeric algorithm for polynomials

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Polynomials, factorization in commutative rings (13P05)

Related Items

Relaxed NewtonSLRA for approximate GCD ⋮ SLRA Interpolation for Approximate GCD of Several Multivariate Polynomials

Uses Software

• GPGCD

Cites Work

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• GPGCD: an iterative method for calculating approximate GCD of univariate polynomials
• Approximate polynomial GCD over integers
• The ERES method for computing the approximate GCD of several polynomials
• Approximate polynomial GCD: small degree and small height perturbations
• Quasi-gcd computations
• Approximate GCD and its application to ill-conditioned algebraic equations
• Certified approximate univariate GCDs
• New fast Euclidean algorithms
• Variable projection methods for approximate (greatest) common divisor computations
• A non-linear structure-preserving matrix method for the computation of the coefficients of an approximate greatest common divisor of two Bernstein polynomials
• An ODE-based method for computing the approximate greatest common divisor of polynomials
• Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials
• Structured Matrix Based Methods for Approximate Polynomial GCD
• The numerical greatest common divisor of univariate polynomials
• Calculation of Zeros of a Real Polynomial Through Factorization Using Euclid’s Algorithm
• Stable and Efficient Algorithms for Structured Systems of Linear Equations
• Computing the Nearest Rank-Deficient Matrix Polynomial
• Extended QRGCD Algorithm
• <tex>$QR$</tex>Factoring to Compute the GCD of Univariate Approximate Polynomials
• Another Theorem Relating Sylvester's Matrix and the Greatest Common Divisor