2014/02/17 by James Brannick, Brannick, James, Karsten Kahl +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1402.4005
openalex publication_date 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a natural choice for solving these systems. In this paper we investigate extensions and improvements of the bootstrap algebraic multigrid framework for solving these systems. This is achieved by reworking the bootstrap setup process to use singular vectors instead of eigenvectors in constructing interpolation and restriction. We formulate a result concerning the convergence speed of GMRES for singular systems and experimentally justify why rapid convergence of the proposed method can be expected. We demonstrate its fast convergence and the favorable scaling behavior for various test problems.