Open AccessAlgorithm for the set of similarity criteria formation for a physical process in the class of homogeneous functions
Author(s) -
А.П. Алпатов,
Victor Kravets,
Dmytro Kolosov,
V. L. Kravets,
Erik Lapkhanov
Publication year - 2021
Publication title -
transactions on machine learning and artificial intelligence
Language(s) - English
Resource type - Journals
ISSN - 2054-7390
DOI - 10.14738/tmlai.96.11295
Subject(s) - similarity (geometry) , set (abstract data type) , class (philosophy) , computer science , homogeneous , table (database) , algebraic number , algorithm , process (computing) , mathematics , theoretical computer science , algebra over a field , data mining , artificial intelligence , combinatorics , pure mathematics , mathematical analysis , image (mathematics) , programming language , operating system
The efficiency of application of linear programming methods to problems of the theory of similarity and dimensions is shown. A general algorithm for formation of the set of similarity criteria for a physical process in the class of homogeneous functions is proposed. The set of systems of linear algebraic equations is created using the combinatorial method and chain diagrams. Basic and free variables and their corresponding variants of dimensionless sets of independent arguments, which are taken as the main similarity criteria, are distinguished. The set of derived similarity criteria is found using the basic criteria and the Cayley table.