Matrix methods for the tensorial Bernstein form

DOI10.1016/j.amc.2018.08.049zbMath1429.65125OpenAlexW2898969359MaRDI QIDQ2008413

Jürgen Garloff, Jihad Titi

Publication date: 25 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-2-vkvev3pxnwe20

zbMATH Keywords

subdivisionrange enclosureinterval polynomialBernstein coefficienttensorial Bernstein form

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Derivative-free methods and methods using generalized derivatives (90C56)

Related Items (3)

Bounds for the range of a complex polynomial over a rectangular region ⋮ On the Hurwitz stability of noninteger Hadamard powers of stable polynomials ⋮ A subdivision algorithm to reason on high-degree polynomial constraints over finite domains

Cites Work

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• Global optimization of mixed-integer nonlinear (polynomial) programming problems: The Bernstein polynomial approach
• The Bernstein polynomial basis: a centennial retrospective
• An improved Bernstein global optimization algorithm for MINLP problems with application in process industry
• On computing Bézier curves by Pascal matrix methods
• Constrained global optimization of multivariate polynomials using Bernstein branch and prune algorithm
• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• Fast construction of constant bound functions for sparse polynomials
• An efficient algorithm for range computation of polynomials using the Bernstein form
• Optimal computation of the Bernstein algorithm for the bound of an interval polynomial
• Lower bound functions for polynomials
• Bézier and B-spline techniques
• Matrix methods for the simplicial Bernstein representation and for the evaluation of multivariate polynomials
• Formalization of Bernstein polynomials and applications to global optimization
• An improved interval global optimization algorithm using higher-order inclusion function forms
• Introduction to Interval Analysis
• Robustness analysis of polynomials with polynomial parameter dependency using Bernstein expansion
• On the Multivariate Horner Scheme

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