Subdivision algorithms converge quadratically
Journal of Computational and Applied Mathematics
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
On the stability of transformations between power and Bernstein polynomial forms
Computer Aided Geometric Design
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Finding all solutions of nonlinear equations using the dual simplex method
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Lower bound functions for polynomials
Journal of Computational and Applied Mathematics
How good are interior point methods? Klee–Minty cubes tighten iteration-complexity bounds
Mathematical Programming: Series A and B
Fast construction of constant bound functions for sparse polynomials
Journal of Global Optimization
Introduction to Interval Analysis
Introduction to Interval Analysis
Nonlinear systems solver in floating-point arithmetic using LP reduction
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Making adaptive an interval constraint propagation algorithm exploiting monotonicity
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
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Polynomial ranges are commonly used for numerically solving polynomial systems with interval Newton solvers. Often ranges are computed using the convex hull property of the tensorial Bernstein basis, which is exponential size in the number n of variables. In this paper, we consider methods to compute tight bounds for polynomials in n variables by solving two linear programming problems over a polytope. We formulate a polytope defined as the convex hull of the coefficients with respect to the tensorial Bernstein basis, and we formulate several polytopes based on the Bernstein polynomials of the domain. These Bernstein polytopes can be defined by a polynomial number of halfspaces. We give the number of vertices, the number of hyperfaces, and the volume of each polytope for n=1,2,3,4, and we compare the computed range widths for random n-variate polynomials for n=