A note on the Bernstein algorithm for bounds for interval polynomials

Rokne, Jon G.

doi:10.1007/bf02253136

Cited by 10 publications

(1 citation statement)

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“…Horner form [15], [110] reduces overestimation of interval polynomial evaluation. Bernstein form [26], [41], [45], [97], [100] bounds polynomials by ranges of Bernstein coefficients. Taylor model [10], [11], [74], [75] changes coefficients of Taylor form from intervals to real numbers.…”

Section: Polynomial Enclosurementioning

confidence: 99%

Solving Interval Constraints by Linearization in Computer-Aided Design

Wang

Nnaji

2006

Reliable Comput

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Current parametric CAD systems require geometric parameters to have fixed values. Specifying fixed parameter values implicitly adds rigid constraints on the geometry, which have the potential to introduce conflicts during the design process. This paper presents a soft constraint representation scheme based on nominal interval. Interval geometric parameters capture inexactness of conceptual and embodiment design, uncertainty in detail design, as well as boundary information for design optimization. To accommodate under-constrained and over-constrained design problems, a double-loop Gauss-Seidel method is developed to solve linear constraints. A symbolic preconditioning procedure transforms nonlinear equations to separable form. Inequalities are also transformed and integrated with equalities. Nonlinear constraints can be bounded by piecewise linear enclosures and solved by linear methods iteratively. A sensitivity analysis method that differentiates active and inactive constraints is presented for design refinement.

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Section: Polynomial Enclosurementioning

confidence: 99%