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Efficient computation of sparse approximate inverses
Author(s) -
Huckle Thomas K.
Publication year - 1998
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199801/02)5:1<57::aid-nla129>3.0.co;2-c
Subject(s) - computation , sparse matrix , mathematics , norm (philosophy) , sparse approximation , inverse , column (typography) , matrix (chemical analysis) , algorithm , matrix norm , iterative method , least squares function approximation , mathematical optimization , eigenvalues and eigenvectors , statistics , physics , geometry , materials science , quantum mechanics , connection (principal bundle) , political science , law , composite material , gaussian , estimator
We investigate different methods for computing a sparse approximate inverse M for a given sparse matrix A by minimizing ∥ AM − E ∥ in the Frobenius norm. Such methods are very useful for deriving preconditioners in iterative solvers, especially in a parallel environment. We compare different strategies for choosing the sparsity structure of M and different ways for solving the small least squares problem that are related to the computation of each column of M . Especially we show how we can take full advantage of the sparsity of A . © 1998 John Wiley & Sons, Ltd.