Range bounding with Taylor models: some case studies

Authors:
Kyoko Makino;Martin Berz;Youn-Kyung Kim
Affiliations:
Department of Physics and Astronomy, Michigan State University, East Lansing, MI;Department of Physics and Astronomy, Michigan State University, East Lansing, MI;Department of Physics and Astronomy, Michigan State University, East Lansing, MI
Venue:
Math'04 Proceedings of the 5th WSEAS International Conference on Applied Mathematics
Year:
2004

Citing 2
Cited 0

An Algorithm for Global Optimization using the Taylor–Bernstein Form as Inclusion Function

Journal of Global Optimization
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)

Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)

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Abstract

Taylor model methods represent a combination of high-order multivariate automatic differentiation and the simultaneous computation of an interval remainder bound enclosing approximation error over a given domain. This method allows a far-reaching suppression of the dependency problem common to interval methods, and can thus often be used for precise range bounding problems. We compare the performance of the method with other state of the art validated tools including centered forms and mean value forms. We also compare with the computation of remainder bounds via high-order interval automatic differentiation.