The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials

DOI10.1016/j.apnum.2016.08.005zbMath1353.65014OpenAlexW2513773657MaRDI QIDQ338517

Su Yi, Martin Bourne, Winkler, Joab R.

Publication date: 7 November 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: http://eprints.whiterose.ac.uk/104349/1/winkler.pdf

zbMATH Keywords

singular value decompositionBernstein polynomialsQR decompositionBézout matrixSylvester resultant matrixapproximate greatest common divisor

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Numerical linear algebra (65F99) Solving polynomial systems; resultants (13P15)

Related Items

A non-linear structure-preserving matrix method for the computation of the coefficients of an approximate greatest common divisor of two Bernstein 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 ⋮ The computation of the greatest common divisor of three bivariate Bernstein polynomials defined in a rectangular domain ⋮ The Computation of Multiple Roots of a Bernstein Basis Polynomial ⋮ Numerical analysis of fractional viscoelastic column based on shifted Chebyshev wavelet function

Uses Software

• BPOLY
• MultRoot
• na25

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Computing curve intersection by means of simultaneous iterations
• A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix
• Certified approximate univariate GCDs
• 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
• QR-factorization method for computing the greatest common divisor of polynomials with inexact coefficients
• Polynomial Scaling
• <tex>$QR$</tex>Factoring to Compute the GCD of Univariate Approximate Polynomials
• Algorithm 812: BPOLY

This page was built for publication: The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials