The Taylor Models are mathematical tools that enable the rigorous representation of functions by a polynomial expansion and a remainder that encloses all sources of errors. These kinds of models define it own arithmetic (and composition) of functions in a validated manner, this means that the represented function is guaranteed to be enclosed in some interval.

Several methods can be benefited from these models, of particular interest are the interval optimization problems and the validated solution to ordinary differential equations.

My project consists of improving the existent methods in TaylorModels.jl, a Julia package that implements these models. The improvements include:

  • Algorithms to tightening the enclosure of the represented functions and its applications to interval optimization.
  • A new approach to rigorously solving ordinary differential equations.

Organization

Student

Uziel Linares

Mentors

  • Luis Benet
  • Marcelo Forets
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2020