Journals Information
Universal Journal of Applied Mathematics Vol. 11(2), pp. 28 - 33
DOI: 10.13189/ujam.2023.110202
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Application of Grobner Basis Technique in Economic Models and Markov Process
V.James 1,*, B.Sivakumar 2
1 Department of Mathematics, Rajalakshmi Engineering College, Chennai, India
2 Department of Mathematics, SSN College of Engineering, Chennai, India
ABSTRACT
The past decade has witnessed enormous advances in the applications of matrix algebra in the life sciences. These advances have significant implications for the future practice of economics, Network analysis, Data analysis, Image processing, Optimization problems, and Quantum mechanics. The main objective of matrix algebra is to solve a system of equations using classical algorithm methods like Gauss elimination or matrix inversion. In recent years, handling a large number of data or finding the solutions to a large number of systems of equations is one of the problems in matrix algebra techniques. One of the effective methods to solve system of polynomial is Grobner basis techniques. It is a powerful tool in matrix algebra and in this method the leading terms of the polynomials are eliminated until no further reductions are possible. The objective of this paper is to solve Input-Output economic problems using the Grobner basis method which is one of the matrix algebra techniques. In real world, many decisions are taken based on the output of Input-Output table or Leontief models problems which have a large number of data or industries. There are two types of Leontief models, namely closed and open models. In this article, we consider the closed Leontief model. Also, we present one simple algorithm based on Grobner basis techniques to find the solution of a system of equations that occur on the Markov model.
KEYWORDS
Input-Output Economics, Open Model, Grobner Basis, Buchberger Algorithm, Markov Process, Transition Probabilities
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] V.James , B.Sivakumar , "Application of Grobner Basis Technique in Economic Models and Markov Process," Universal Journal of Applied Mathematics, Vol. 11, No. 2, pp. 28 - 33, 2023. DOI: 10.13189/ujam.2023.110202.
(b). APA Format:
V.James , B.Sivakumar (2023). Application of Grobner Basis Technique in Economic Models and Markov Process. Universal Journal of Applied Mathematics, 11(2), 28 - 33. DOI: 10.13189/ujam.2023.110202.