Open AccessResults on the effect of orderings on SSOR and ILU preconditionings
Author(s) -
Wayne Joubert,
Emanuel Knill
Publication year - 1998
Language(s) - English
Resource type - Reports
DOI - 10.2172/348916
Subject(s) - rate of convergence , robustness (evolution) , inverse , mathematics , parallelism (grammar) , convergence (economics) , computer science , algorithm , parallel computing , chemistry , geometry , computer network , biochemistry , channel (broadcasting) , economics , gene , economic growth
It is known that for SSOR and ILU preconditionings for solving systems of linear equations, orderings can have an enormous impact on robustness, convergence rate and parallelism. Unfortunately, it has been observed that there is an inverse relation between the convergence rate and the parallelism of typical orderings used in practice. This paper presents some numerical experiments with simple matrices to illustrate this behavior as well as a new theoretical result which sheds some light on this phenomenon and also gives an upper bound on the convergence rate of a number of preconditioners in popular use