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JuliaIntervals / TaylorModels.jl

Rigorous function approximation using Taylor models in Julia
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Better bound for Taylor Model product #80

Open ulinares opened 4 years ago

ulinares commented 4 years ago

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

tmprod

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

lbenet commented 4 years ago

Excellent! Can you make a PR?

lbenet commented 4 years ago

I think it is worth the extra evaluation and the intersection...