Conditioning analysis of incomplete Cholesky factorizations with orthogonal droppingperNapov, ArtemorgLawrence Berkeley National Laboratory. Computational Research Division.Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (United States)Berkeley, CaliforniaLawrence Berkeley National Laboratory2012-03-16engThe 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.3697 Mathematics And Computing Incomplete Cholesky, Conditioning Analysis, Convergence Analysis, Iterative Methods, PreconditionerIncomplete Cholesky, Conditioning Analysis, Convergence Analysis, Iterative Methods, Preconditioner