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]."
}