New Applications of Taylor Model Methods
AbstractTaylor 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.
K. Makino, M. Berz, in: "Automatic Differentiation: From Simulation to Optimization", G. Corliss, C. Faure, A. Griewank, L. Hascoet, U. Naumann (Eds.) (2001) Springer
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