Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Journal of Computational and Applied Mathematics - Special issue on extrapolation and rational approximation
Algorithm for implicitizing rational parametric surfaces
Computer Aided Geometric Design
Multipolynomial resultant algorithms
Journal of Symbolic Computation
Comparison of various multivariate resultant formulations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Matrix computations (3rd ed.)
Implicitizing rational curves by the method of moving algebraic curves
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Modern computer algebra
An object-oriented platform for distributed high-performance symbolic computation
Mathematics and Computers in Simulation - Special issue on high performance symbolic computing
The ubiquitous Kronecker product
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Tracing index of rational curve parametrizations
Computer Aided Geometric Design
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Real-time computer control of a multilevel converter using the mathematical theory of resultants
Mathematics and Computers in Simulation - Special issue: Modelling and simulation of electrical machines, converters and systems
The Kronecker product and stochastic automata networks
Journal of Computational and Applied Mathematics
Symmetric functions and the Vandermonde matrix
Journal of Computational and Applied Mathematics
Automatic determination of envelopes and other derived curves within a graphic environment
Mathematics and Computers in Simulation - Special issue: Applications of computer algebra in science, engineering, simulation and special software
Using polynomial interpolation for implicitizing algebraic curves
Computer Aided Geometric Design
Real implicitization of curves and geometric extraneous components
Proceedings of the 2007 international workshop on Symbolic-numeric computation
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A non-standard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered, and their respective computational complexities are analyzed. Although the techniques employed are usually associated to numerical analysis, in this case all the computations are carried out using exact rational arithmetic. The power of the Kronecker product of matrices in this application is stressed.