Affine Arithmetic


Title: Affine Arithmetic
Author: Fabian Immler
Submission date: 2014-02-07
Abstract: We give a formalization of affine forms as abstract representations of zonotopes. We provide affine operations as well as overapproximations of some non-affine operations like multiplication and division. Expressions involving those operations can automatically be turned into (executable) functions approximating the original expression in affine arithmetic.
Change history: [2015-01-31]: added algorithm for zonotope/hyperplane intersection
[2017-09-20]: linear approximations for all symbols from the floatarith data type
  author  = {Fabian Immler},
  title   = {Affine Arithmetic},
  journal = {Archive of Formal Proofs},
  month   = feb,
  year    = 2014,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Deriving, List-Index, Show
Used by: Ordinary_Differential_Equations, Taylor_Models