Publication: New Applications of Taylor Model Methods
Introduction
Applications
Tools
Research Groups
Workshops
Publications
   List Publications
   Advanced Search
   Info
   Add Publications
My Account
About

New Applications of Taylor Model Methods

- incollection -
 

Author(s)
Kyoko Makino , Martin Berz

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
Taylor model methods unify many concepts of high-order computational differentiation with verification approaches covering the Taylor remainder term. Not only do they provide local multivariate derivatives, they also allow for highly efficient and sharp verification. We present several recent results obtained with Taylor model methods, including verified optimization, verified quadrature and verified propagation of extended domains of initial conditions through ODEs, approaches towards verified solution of DAEs and PDEs. In all cases, the methods allow the development of new numeric-analytic tools that efficiently capitalize on the availability of derivatives and sharp inclusions over extended ranges. Applications of the methods are given, including global optimization, very high-dimensional numeric quadrature, particle accelerators, and dynamics of near-earth asteroids.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Makino2002NAo,
       author = "Kyoko Makino and Martin Berz",
       title = "New Applications of {T}aylor Model Methods",
       pages = "359--364",
       crossref = "Corliss2002ADo",
       abstract = "Taylor model methods unify many concepts of high-order computational
         differentiation with verification approaches covering the Taylor remainder term. Not only do they
         provide local multivariate derivatives, they also allow for highly efficient and sharp verification.
         We present several recent results obtained with Taylor model methods, including verified
         optimization, verified quadrature and verified propagation of extended domains of initial conditions
         through ODEs, approaches towards verified solution of DAEs and PDEs. In all cases, the methods allow
         the development of new numeric-analytic tools that efficiently capitalize on the availability of
         derivatives and sharp inclusions over extended ranges. Applications of the methods are given,
         including global optimization, very high-dimensional numeric quadrature, particle accelerators, and
         dynamics of near-earth asteroids.",
       chapter = "43",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       referred = "[Kearfott2002TSM]."
}


back
  

Contact:
autodiff.org
Username:
Password:
(lost password)