mathcal FAINV hierarchically factored appro

Authors: R Kriemann S Le Borne

Publish Date: 2015/12/29

Volume: 17, Issue: 3, Pages: 135-150

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Abstract

Given a sparse matrix its LUfactors inverse and inverse factors typically suffer from substantial fillin leading to nonoptimal complexities in their computation as well as their storage In the past several computationally efficient methods have been developed to compute approximations to these otherwise rather dense matrices Many of these approaches are based on approximations through sparse matrices leading to wellknown ILU sparse approximate inverse or factored sparse approximate inverse techniques and their variants A different approximation approach is based on blockwise low rank approximations and is realized for example through hierarchical mathcal H matrices While mathcal Hinverses and mathcal HLU factors have been discussed in the literature this paper will consider the construction of an approximation of the factored inverse through mathcal Hmatrices mathcal HFAINV We will describe a blockwise approach that permits to replace exact matrix arithmetic through approximate efficient mathcal Harithmetic We conclude with numerical results in which we use approximate factored inverses as preconditioners in the iterative solution of the discretized convection–diffusion problem

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