Algorithms, computations and structural information

Abstract In a wide class of problems, symbolic models approach yields results in more convenient form and even more accurate than in pure numerical approximations. Some constructive methods can be considered as ready-to-use symbolic algorithms solving particular problems. Direct implementation of such mathematical objects brings computational difficulties. Hence, these methods require optimization and detailed analysis from computational point of view, that may be achieved by a proper integration of both symbolic computations and numerical algorithms. In this chapter we review the spectrum of computational methods and algorithms arisen in the process of solving analytical problems presented in the book. We also focus on the information aspect of the computational materials science. In particular, we present the scheme of extracting new information processing tools from computational sciences and realize the scheme by deriving features for structural information of configurations of objects on the plane.