Optimized refinable enclosures of multivariate polynomial pieces

✍ Scribed by David Lutterkort; Jörg Peters

• Book ID: 104304892
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 395 KB
• Volume: 18
• Category: Article
• ISSN: 0167-8396
• DOI: 10.1016/s0167-8396(01)00067-x

✦ Synopsis

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 max U b +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 < dim B pre-optimized enclosures and linearly combining them with the second differences of b. The width of these enclosures scales by a factor 1/4 under midpoint subdivision.