On the stability of transformations between power and Bernstein polynomial forms
Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Displacement structure: theory and applications
SIAM Review
Backward error analysis of Neville elimination
Applied Numerical Mathematics
Tracing index of rational curve parametrizations
Computer Aided Geometric Design
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Theoretical Computer Science - Algebraic and numerical algorithm
Improved algorithms for computing determinants and resultants
Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
The Accurate and Efficient Solution of a Totally Positive Generalized Vandermonde Linear System
SIAM Journal on Matrix Analysis and Applications
Optimal properties of the uniform algebraic trigonometric B-splines
Computer Aided Geometric Design
Using polynomial interpolation for implicitizing algebraic curves
Computer Aided Geometric Design
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A new application of Bernstein-Bezoutian matrices, a type of resultant matrices constructed when the polynomials are given in the Bernstein basis, is presented. In particular, the approach to curve implicitization through Sylvester and Bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case in which the polynomials appearing in the rational parametric equations of the curve are expressed in the Bernstein basis, avoiding the basis conversion from the Bernstein to the power basis. The coefficients of the implicit equation are computed in the bivariate tensor-product Bernstein basis, and their computation involves the bidiagonal factorization of the inverses of certain totally positive matrices.