Higher Order Verified Inclusions of Multidimensional Systems by Taylor Models
AbstractDifferent from floating point computations, interval methods provide
rigorous enclosures of functions, however the limitation of the
methods is the overestimation mostly caused by the lack of information
on functional dependency. The first cure to the problem is to use a
smaller domain, but when a function is complicated, as it often is for
practical problems, the number of subdivisions becomes quite large. In
case of multidimensional systems, the computational expense by simple
interval methods increases astronomically. A new approach, the Taylor
model method, models a function by a higher order polynomial which
keeps the majority of the functional dependency, and an interval which
contains the small remaining error. The method naturally suppresses
the dependency problem, and proves particularly effective for the
treatment of complicated multidimensional systems.
K. Makino, M. Berz, Nonlinear Analysis 47 (2001) 3503-3514
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