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Direct Equation Solving Methods Algorithms Compositions of Lower-Upper Triangular Matrix and Grassmann-Taksar-Heyman for the Stationary Distribution of Markov Chains

  • Sunday Olanrewaju Agboola
The modelled system is believed to have only one state at any given time, and its evolution is represented by transitions from one state to the next. This system's physical or mathematical behavior can also be depicted by defining all of the numerous states it can be in and demonstrating how it moves between them. In this study, the direct equation methods for the stationary distribution of Markov chains which produce a significantly more accurate response in less time for some types of situations and also, tries to get to the end result as quickly as possible, while the solution must be computed when a specified number of well-defined stages have been completed has been investigated, in order to provide some insight into the solutions of stationary distribution of Markov chain. Our quest is to compute the solutions and algorithms for Gaussian elimination method, lower - upper triangular matrix approach and the Grassmann - Taksar - Heyman advantage which is an extension of Gaussian elimination. Matrix operations are used with the help of some existing laws, theorems and formulas of Markov chain. The stationary distribution vector’s π_i,i=1,2,…,n are obtained.
Select Volume / Issue:
Year:
2021
Type of Publication:
Article
Keywords:
Gaussian Elimination; Grassmann-Taksar-Heyman; Infinitesimal Generator; Lower-Upper Triangular Matrix
Journal:
IJASM
Volume:
8
Number:
6
Pages:
87-96
Month:
November
ISSN:
2394-2894
Hits: 1809
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