An Axiomatic Research Method of Computational Math’s on the Example of the Problem of Choosing a Method for Calculating the Specific Weight of Factors in Multiplicative Index Models)
The study provides a general scheme of comparative analysis and selection of methods for solving problems of applied mathematics based on the axiomatic approach. This approach is based on the representation of computational methods in the form of mapping the initial data into the desired results. A priori, a wide class of such mappings is introduced, which certainly contains all known and potentially possible methods for solving this problem. Then the authors formulated substantively necessary and mathematically strict requirements for these mappings, i.e. the properties of methods and models that should be used to solve it. On the basis of theoretical studies, we determined the mappings that satisfy all the introduced requirements, or establish the absence of a method that satisfies all of them, which means the inconsistency of the requirements. The author explored the problem of choosing methods for calculating the specific weights of economic indexes-factors in the resulting index, which is the product of indexes-factors. In this case, the initial set of computational methods consists of mappings n-dimensional vectors with positive components (sets of initial factor indices, where n their number is) to n-dimensional vectors with all positive coefficients, the components of which mean the calculated share of each of the factor indices in their product. The author discusses and formulates the system of requirements for the methods for calculating the specific weights of index-factors. A theorem is put forward according to which all these requirements are fulfilled if and only if the specific weights are calculated by the so-called logarithmic method, i.e. as a result of dividing the logarithm of the index-factors by the logarithm of the resulting index. The article considers the problem of possible redundancy of requirements.