Improvements on the hybrid Monte Carlo algorithms for matrix computations

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Fathi-Vajargah B., Hassanzadeh Z.

Sadhana - Academy Proceedings in Engineering Sciences, cilt.44, sa.1, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s12046-018-0983-y
  • Dergi Adı: Sadhana - Academy Proceedings in Engineering Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: convergence analysis, Markov chain Monte Carlo, matrix inversion, System of linear algebraic equations, transition probability
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

In this paper, we present some improvements on the Markov chain Monte Carlo and hybrid Markov chain Monte Carlo algorithms for matrix computations. We discuss the convergence of the Monte Carlo method using the Ulam–von Neumann approach related to selecting the transition probability matrix. Specifically, we show that if the norm of the iteration matrix T is less than 1 then the Monte Carlo Almost Optimal method is convergent. Moreover, we suggest a new technique to approximate the inverse of the strictly diagonally dominant matrix and we exert some modifications and corrections on the hybrid Monte Carlo algorithm to obtain the inverse matrix in general. Finally, numerical experiments are discussed to illustrate the efficiency of the theoretical results.