Matrix methods for the tensorial Bernstein form
نویسندگان
چکیده
منابع مشابه
Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form
A method is investigated by which tight bounds on the range of a multivariate rational function over a box can be computed. The approach relies on the expansion of the numerator and denominator polynomials in Bernstein polynomials. Convergence of the bounds to the range with respect to degree elevation of the Bernstein expansion, to the width of the box and to subdivision are proven and the inc...
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The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n= 6 or 7 variables. This article describes a polytope (...
متن کاملMatrix methods for the simplicial Bernstein representation and for the evaluation of multivariate polynomials
In this paper, multivariate polynomials in the Bernstein basis over a simplex (simplicial Bernstein representation) are considered. Two matrix methods for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, are presented. Also matrix methods for the calculation of the Bernstein coefficients over subsimplices generated by subd...
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The paper describes a method to compute a basis of mutually orthogonal polynomials with respect to an arbitrary Jacobi weight on the simplex. This construction takes place entirely in terms of the coefficients with respect to the so–called Bernstein–Bézier form of a polynomial.
متن کاملConvergence of the Simplicial Rational Bernstein Form
Bernstein polynomials on a simplex V are considered. The expansion of a given polynomial p into these polynomials provides bounds for the range of p over V . Bounds for the range of a rational function over V can easily obtained from the Bernstein expansions of the numerator and denominator polynomials of this function. In this paper it is shown that these bounds converge monotonically and line...
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2019
ISSN: 0096-3003
DOI: 10.1016/j.amc.2018.08.049