Evolutionary Optimization for Algebraic Varieties, Design of Robust Runge-Kutta Methods

Details Evolutionary Optimization for Algebraic Varieties, Design of Robust Runge-Kutta Methods Evolutionary Optimization for Algebraic Varieties, Design of Robust Runge-Kutta Methods

2011-10-05

arxiv.org/abs/1110.1120v1

Mathematics

Algebraic Geometry

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Scientific paper

This work presents a new evolutionary optimization algorithm in theoretical mathematics with important applications in scientific computing. The use of the evolutionary algorithm is justified by the difficulty of the study of the parametrization of an algebraic variety, an important problem in algebraic geometry. We illustrate an application, Evo-Runge-Kutta, in a problem of numerical analysis. Results show the design and the optimization of particular algebraic variety, the explicit s levels Runge-Kutta methods of order q. The mapping between algebraic geometry and evolutionary optimization is direct, and we expect that many open problems will be modelled in the same way.

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