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Higher Order Verified Inclusions of Multidimensional Systems by Taylor Models


Abstract

Different 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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