Playing around with the implementation of the product of Taylor Models given in [1],
I found that his implementation gives a better bound for the resulting Taylor Model, eg, the TaylorModel1 product for f(x) = sin(x), g(x)=cos(x) + x^3, gives the following results
Green boxes correspond to the case where the diameter of the bound given by the current implementation is equal
to the diameter of the bound given by the implementation in [1].
Red boxes correspond to the case where the diameter of the bound given by [1] is less than the bound given by the
current implementation.
What do you think about this @lbenet?
[1] A Taylor model toolbox for solving ODEs implemented in MATLAB/INTLAB, Floarian Bünger
Playing around with the implementation of the product of Taylor Models given in [1],
I found that his implementation gives a better bound for the resulting Taylor Model, eg, the
TaylorModel1product forf(x) = sin(x),g(x)=cos(x) + x^3, gives the following resultsGreen boxes correspond to the case where the diameter of the bound given by the current implementation is equal
to the diameter of the bound given by the implementation in [1].
Red boxes correspond to the case where the diameter of the bound given by [1] is less than the bound given by the
current implementation.
What do you think about this @lbenet?
[1] A Taylor model toolbox for solving ODEs implemented in MATLAB/INTLAB, Floarian Bünger