A companion matrix resultant for Bernstein polynomials

DOI10.1016/S0024-3795(02)00486-XzbMath1042.15006OpenAlexW2042691439MaRDI QIDQ1863577

Winkler, Joab R.

Publication date: 11 March 2003

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(02)00486-x

zbMATH Keywords

stabilitycompanion matrixBernstein polynomialresultantBernstein basisnumerical conditiontriangular Hankel matrix

Mathematics Subject Classification ID

Polynomials in number theory (11C08) Polynomials in general fields (irreducibility, etc.) (12E05) Conditioning of matrices (15A12) Matrices, determinants in number theory (11C20)

Related Items

Linearizations of matrix polynomials in Bernstein bases, Scaled generalized Bernstein polynomials and containment regions for the zeros of polynomials, High-order quadrature on multi-component domains implicitly defined by multivariate polynomials, A non-linear structure-preserving matrix method for the computation of the coefficients of an approximate greatest common divisor of two Bernstein polynomials, Bernstein-Bézoutian matrices, Bernstein Bézoutians and application to intersection problems, The Bernstein polynomial basis: a centennial retrospective, The transformation of the companion matrix resultant between the power and Bernstein polynomial bases., Basis-Independent Polynomial Division Algorithm Applied to Division in Lagrange and Bernstein Basis, Block \(\mathbf {LU}\) factors of generalized companion matrix pencils, A unified approach to resultant matrices for Bernstein basis polynomials, The Computation of Multiple Roots of a Bernstein Basis Polynomial

Uses Software

• mctoolbox

Cites Work

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• The Cayley method in computer aided geometric design
• Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves
• Quasi-gcd computations
• On the numerical condition of polynomials in Bernstein form
• Approximate GCD and its application to ill-conditioned algebraic equations
• The transformation of the companion matrix resultant between the power and Bernstein polynomial bases.
• Best linear common divisors for approximate degree reduction
• Efficient Algorithms for MultiPolynomial Resultant
• Algorithms for intersecting parametric and algebraic curves I
• On the optimal stability of the Bernstein basis
• Polynomial Roots from Companion Matrix Eigenvalues
• A resultant matrix for scaled Bernstein polynomials