A new Monte Carlo method for solving system of linear algebraic equations

Fathi-Vajargah B., Hassanzadeh Z.

Computational Methods for Differential Equations, vol.9, no.1, pp.159-179, 2021 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.22034/cmde.2020.30640.1453
  • Journal Name: Computational Methods for Differential Equations
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.159-179
  • Keywords: Ergodic Markov chain, Monte Carlo method, Spectral radius, System of linear algebraic equations, Transition probability matrix
  • Istanbul Gelisim University Affiliated: No

Abstract

In this paper, we firstly study the employing of the Monte Carlo method for solving system of linear algebraic equations and then analyze on convergence of this method. We propound new results related to the convergence of the Monte Carlo method. Additionally, we introduce a new Monte Carlo algorithm with effective techniques. Finally, we compare the efficiency of new Monte Carlo algorithm with its old version in the numerical experiments.