A Bootstrap Algebraic Multilevel Method for Markov Chains

A Bootstrap Algebraic Multilevel Method for Markov Chains

This work concerns the development of an algebraic multilevel method for computing state vectors of Markov chains. We present an efficient bootstrap algebraic multigrid method for this task. In our proposed approach, we employ a multilevel eigensolver, with interpolation built using ideas based on compatible relaxation, algebraic distances, and least squares fitting of test vectors. Our adaptiv...

Algebraic Multigrid for Markov Chains

An algebraic multigrid (AMG) method is presented for the calculation of the stationary probability vector of an irreducible Markov chain. The method is based on standard AMG for nonsingular linear systems, but in a multiplicative, adaptive setting. A modified AMG interpolation formula is proposed that produces a nonnegative interpolation operator with unit row sums. We show how the adoption of ...

Approximate regenerative-block bootstrap for Markov chains

Recursively Accelerated Multilevel Aggregation for Markov Chains

A recursive acceleration method is proposed for multiplicative multilevel aggregation algorithms that calculate the stationary probability vector of large, sparse and irreducible Markov chains. Pairs of consecutive iterates at all branches and levels of a multigrid W cycle with simple, nonoverlapping aggregation are recombined to produce improved iterates at those levels. This is achieved by so...

Fast multilevel methods for Markov chains

This paper describes multilevel methods for the calculation of the stationary probability vector of large, sparse, irreducible Markov chains. In particular, several recently proposed significant improvements to the multilevel aggregation method of Horton and Leutenegger are described and compared. Furthermore, we propose a very simple improvement of that method using an over-correction mechanis...