Efficient Control of the Dependency Problem Based on Taylor Model Methods

It is shown how the Taylor Model approach allows the rigorous description of functional dependencies with far-reaching control of the dependency problem. The amount of overestimation decreases with a high power of the interval over which the information is required, at a computational expense that increases rather moderately with the dimensionality of the problem. This leads to the possibility of treating even cases with a very significant dependency problem that are intractable using conventional methods.