Multiaspectness and Localization

One of the main objectives of interval mathematics is to produce an interval that contains the solution to a given mathematical problem (i.e., the Cauchy problem). There exist methods that produce ellipsoids, parallelepipeds, and other types of sets that contain the same solution. To get a better estimate, it is natural to consider the intersection of sets belonging to different classes of mathematical objects as a localization of the desired solution. In this paper, we propose new data types that help to implement this idea in programming. The use of these data types also helps to organize an interface between sumbolic and numerical computations, and to parallelize the resulting program.