Optimized refinable enclosures of multivariate polynomial pieces Original Research Article

An enclosure is a two-sided approximation of a uni- or multivariate function b∈B by a pair of typically simpler functions b+,b−∈H≠B such that b−⩽b⩽b+ over the domain U of interest. Enclosures are optimized by minimizing the width maxUb+−b− and refined by enlarging the space H. This paper develops a framework for efficiently computing enclosures for multivariate polynomials and, in particular, derives piecewise bilinear enclosures for bivariate polynomials in tensor-product Bézier form. Runtime computation of enclosures consists of looking up s