## Abstract

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 and Leutenegger (Perform. Eval. Rev. 1994; 22:191-200) whereby the coarse-grid problem is adapted to yield a better and better coarse representation of the original problem. A special feature of the present approach is the squaring of the stochastic matrix-followed by a stretching of its spectrum-just prior to the coarse-grid correction process. This procedure is shown to yield good convergence properties, even though a cheap and simple aggregation is used for the restriction and prolongation matrices, which is important for maintaining competitive computational costs. A second special feature is a bottom-up procedure for defining coarse-grid aggregates.

Original language | English |
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Pages (from-to) | 229-251 |

Number of pages | 23 |

Journal | Numerical Linear Algebra with Applications |

Volume | 17 |

Issue number | 2-3 |

DOIs | |

State | Published - 1 Apr 2010 |

Externally published | Yes |

## Keywords

- Algebraic multigrid
- Markov chains
- Smoothed aggregation

## ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics