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Total positivity and least squares problems in the Lagrange basis
Ana Marco, José-Javier Martínez, Raquel Viaña
The problem of polynomial least squares fitting in the standard Lagrange basis is addressed in this work. Although the matrices involved in the corresponding overdetermined linear…
Bidiagonal Decompositions of Vandermonde-Type Matrices of Arbitrary Rank
Jorge Delgado, Plamen Koev, Ana Marco +4
We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among othe…
Bjorck-Pereyra-type methods and total positivity
Jose-Javier Martinez
The approach to solving linear systems with structured matrices by means of the bidiagonal factorization of the inverse of the coefficient matrix is first considered, the starting…
The inversion problem for rational Bézier curves
Ana Marco, José-Javier Martinez
The inversion problem for rational Bézier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct…
Accurate computations with Said-Ball-Vandermonde matrices
Ana Marco, Jose-Javier Martinez
A generalization of the Vandermonde matrices which arise when the power basis is replaced by the Said-Ball basis is considered. When the nodes are inside the interval (0,1), then t…
Accurate numerical linear algebra with Bernstein-Vandermonde matrices
Ana Marco, Jose-Javier Martinez
The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares prob…
Polynomial least squares fitting in the Bernstein basis
Ana Marco, Jose-Javier Martinez
The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix A of the overdetermined system to be…
A fast and accurate algorithm for solving Bernstein-Vandermonde linear sytem
A. Marco, J. J. Martinez
A fast and accurate algorithm for solving a Bernstein-Vandermonde linear system is presented. The algorithm is derived by using results related to the bidiagonal decomposition of t…
Structured matrices in the application of bivariate interpolation to curve implicitization
Ana Marco, Jose-Javier Martinez
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different a…
Curve implicitization in the bivariate tensor-product Bernstein basis
Ana Marco, Jose-Javier Martinez
The approach to curve implicitization through Sylvester and Bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case of Bernstein-Bezo…