Efficient numerical solvers for sparse linear systems are crucial in science and engineering.
One of the fastest methods for solving large-scale sparse linear systems is algebraic …

Applying smoothed aggregation (SA) multigrid to solve a nonsymmetric linear system, Ax=b,
is often impeded by the lack of a minimization principle that can be used as a basis for the …

Algebraic multigrid (AMG) methods are known to be efficient in solving linear systems
arising from the discretization of partial differential equations and other related problems …

Quantifying node centrality in multilayer networks is crucial for identifying influential nodes
across various applications. Building on the PageRank model for single-layer networks, Lv …

Abstract Model reduction of large Markov chains is an essential step in a wide array of
techniques for understanding complex systems and for efficiently learning structures from …

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 …

Tensor structured Markov chains are part of stochastic models of many practical
applications, eg, in the description of complex production or telephone networks. The most …

A novel multigrid algorithm for computing the principal eigenvector of column‐stochastic
matrices is developed. The method is based on an approach originally introduced by Horton …

Recently, the adaptive algebraic aggregation multigrid method has been proposed for
computing stationary distributions of Markov chains. This method updates aggregates on …

This paper describes multilevel methods for the calculation of the stationary probability
vector of large, sparse, irreducible Markov chains. In particular, several recently proposed …