The infinity computer vs. Symbolic computations: First steps in comparison

In this contribution, a software simulator of the Infinity Computer is compared with MATLAB's symbolic computations in terms of execution times while solving two applied problems. The aim of this paper is to show advantages of the numerical nature of the Infinity Computer with respect to symbolic computations in solving difficult real-life problems. First, the characteristic polynomials are calculated for matrices of different dimensions. The same algorithm for Laplace expansion is used for both computational frameworks. Two types of matrices are generated randomly: diagonal and dense matrices. In the second application, the Infinity Computer and symbolic computations are compared for exact higher order differentiation of univariate randomly generated functions taken from the literature. For each test function, the first 10 derivatives are calculated and evaluated on a 100 points grid over a preset interval of the domain.