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Title: Conditioning Analysis of Incomplete Cholesky Factorizations with Orthogonal Dropping

The analysis of preconditioners based on incomplete Cholesky factorization in which the neglected (dropped) components are orthogonal to the approximations being kept is presented. General estimate for the condition number of the preconditioned system is given which only depends on the accuracy of individual approximations. The estimate is further improved if, for instance, only the newly computed rows of the factor are modified during each approximation step. In this latter case it is further shown to be sharp. The analysis is illustrated with some existing factorizations in the context of discretized elliptic partial differential equations.
  1. Free Univ. of Brussels (Belgium)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0895-4798
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: SIAM Journal on Metrix Analysis and Applications; Journal Volume: 34; Journal Issue: 3
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING incomplete Cholesky; conditioning analysis; convergence analysis; iterative methods; preconditioner