## ARMS: An Algebraic Recursive Multilevel Solver for general sparse linear systems (1999)

Venue: | Numer. Linear Alg. Appl |

Citations: | 46 - 24 self |

### BibTeX

@TECHREPORT{Saad99arms:an,

author = {Yousef Saad and Brian Suchomel},

title = {ARMS: An Algebraic Recursive Multilevel Solver for general sparse linear systems},

institution = {Numer. Linear Alg. Appl},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper presents a general preconditioning method based on a multilevel partial solution approach. The basic step in constructing the preconditioner is to separate the initial points into two subsets. The first subset which can be termed "coarse" is obtained by using "block" independent sets, or "aggregates". Two aggregates have no coupling between them, but nodes in the same aggregate may be coupled. The nodes not in the coarse set are part of what might be called the "Fringe" set. The idea of the methods is to form the Schur complement related to the fringe set. This leads to a natural block LU factorization which can be used as a preconditioner for the system. This system is then solver recursively using as preconditioner the factorization that could be obtained from the next level. Unlike other multilevel preconditioners available, iterations between levels are allowed. One interesting aspect of the method is that it provides a common framework for many other technique...