A Cost-Effective Smoothed Multigrid with Modified Neighborhood-Based Aggregation for Markov Chains

Abstract EN

Smoothed aggregation multigrid method is considered for computing stationary distributions of Markov chains.

A judgement which determines whether to implement the whole aggregation procedure is proposed.

Through this strategy, a large amount of time in the aggregation procedure is saved without affecting the convergence behavior.

Besides this, we explain the shortage and irrationality of the Neighborhood-Based aggregation which is commonly used in multigrid methods.

Then a modified version is presented to remedy and improve it.

Numerical experiments on some typical Markov chain problems are reported to illustrate the performance of these methods.