On Spectral Clustering in Algebraic Multigrid Methods

Abstract

We introduce a new direct multilevel method for solving general nonsingular complex square linear systems admitting a suitable block partition, using a regular smoother and an arbitrary but equal number of pre- and post-smoothings. Through careful analysis of the error propagation operator, we cluster the spectrum of this operator. This allows us to write a direct K-cycle version of the method.

arXiv comment23 pages, 3 figures