Inversion and spectral analysis of matrices arising in the analysis of Markov processes

Michael N. Katehakis, Laurens C. Smit, Floske M. Spieksma

Research output: Contribution to journalArticlepeer-review


In this paper we provide a novel inversion method and algorithms for nearly tridiagonal matrices arising in the analysis of Markov processes. The method provides a fast and exact computation procedure of the inverse of the matrix that contains the coefficients of a rate matrix of the Markov processes. If the matrix is of countable size, the method provides an exact solution, independent of the truncation size. In contrast, alternative inverse techniques perform much slower and work only for finite size matrices. This leads to more efficient methods to compute the solution to a countable (finite or infinite) set of equations that occurs in queueing systems and in related fields including Markov processes, birth-and-death processes and inventory systems. Furthermore, we provide a procedure to construct the eigenvalues and eigenvectors of an arbitrary matrix, using those of an easier to analyze matrix. We apply and specialize this procedure to the matrix arising in the corresponding Markov rate matrices under consideration.

Original languageEnglish (US)
JournalAnnals of Operations Research
StateAccepted/In press - 2019

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research


  • Eigenvalues
  • Matrix inverse
  • Queueing
  • Stochastic process


Dive into the research topics of 'Inversion and spectral analysis of matrices arising in the analysis of Markov processes'. Together they form a unique fingerprint.

Cite this