A non-linear structure-preserving matrix method for the computation of the coefficients of an approximate greatest common divisor of two Bernstein polynomials

DOI10.1016/j.cam.2017.01.035zbMath1372.65048OpenAlexW2586316509MaRDI QIDQ2400326

Yi Su, Martin Bourne, Winkler, Joab R.

Publication date: 28 August 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://eprints.whiterose.ac.uk/111431/1/BourneWinklerYi.pdf

zbMATH Keywords

Bernstein polynomialscomputer aided geometric designSylvester resultant matrixapproximate greatest common divisorstructure-preserving matrix methods

Mathematics Subject Classification ID

Related Items (8)

Relaxed NewtonSLRA for approximate GCD ⋮ SLRA Interpolation for Approximate GCD of Several Multivariate Polynomials ⋮ An approximate factorisation of three bivariate Bernstein basis polynomials defined in a triangular domain ⋮ The computation of the degree of the greatest common divisor of three Bernstein basis polynomials ⋮ Toward the best algorithm for approximate GCD of univariate polynomials ⋮ The computation of the greatest common divisor of three bivariate Bernstein polynomials defined in a rectangular domain ⋮ The Sylvester and Bézout resultant matrices for blind image deconvolution ⋮ The Computation of Multiple Roots of a Bernstein Basis Polynomial

Uses Software

• BPOLY
• MultRoot

Cites Work

• Implicitizing rational surfaces using moving quadrics constructed from moving planes
• The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials
• The computation of multiple roots of a polynomial
• An improved non-linear method for the computation of a structured low rank approximation of the Sylvester resultant matrix
• Bernstein-Bézoutian matrices
• Two methods for the calculation of the degree of an approximate greatest common divisor of two inexact polynomials
• A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix
• Common factor detection and estimation
• A companion matrix resultant for Bernstein polynomials
• Resultant matrices and the computation of the degree of an approximate greatest common divisor of two inexact Bernstein basis polynomials
• Structured matrix methods for the computation of multiple roots of a polynomial
• The Viro method for construction of \(C^r\) piecewise algebraic hypersurfaces
• The Viro method for construction of Bernstein-Bézier algebraic hypersurface piece
• Structured Total Least Norm for Nonlinear Problems
• DISPLACEMENT STRUCTURE IN COMPUTING APPROXIMATE GCD OF UNIVARIATE POLYNOMIALS
• Algorithm 812: BPOLY
• A resultant matrix for scaled Bernstein polynomials
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• Unnamed Item
• Unnamed Item
• Unnamed Item

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