Taylor Models

 

Title: Taylor Models
Authors: Christoph Traut and Fabian Immler
Submission date: 2018-01-08
Abstract: We present a formally verified implementation of multivariate Taylor models. Taylor models are a form of rigorous polynomial approximation, consisting of an approximation polynomial based on Taylor expansions, combined with a rigorous bound on the approximation error. Taylor models were introduced as a tool to mitigate the dependency problem of interval arithmetic. Our implementation automatically computes Taylor models for the class of elementary functions, expressed by composition of arithmetic operations and basic functions like exp, sin, or square root.
BibTeX:
@article{Taylor_Models-AFP,
  author  = {Christoph Traut and Fabian Immler},
  title   = {Taylor Models},
  journal = {Archive of Formal Proofs},
  month   = jan,
  year    = 2018,
  note    = {\url{https://isa-afp.org/entries/Taylor_Models.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Affine_Arithmetic