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This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient-type methods. Some theoretical… (More)

This paper describes a technique for constructing robust preconditioners for the CGLS method applied to the solution of large and sparse least squares problems. The algorithm computes an incomplete LDL T factorization of the normal equations matrix without the need to form the normal matrix itself. The preconditioner is reliable (pivot breakdowns cannot… (More)

SUMMARY We present two new ways of preconditioning sequences of nonsymmetric linear systems in the special case where the implementation is matrix-free. Both approaches are fully algebraic, they are based on the general updates of incomplete LU decompositions recently introduced in [1], and they may be directly embedded into nonlinear algebraic solvers. The… (More)

A method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix A is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations. It is proved that in exact arithmetic the preconditioner is well defined if A is an H-matrix. The… (More)

Standard preconditioners, like incomplete factorizations, perform well when the coeecient matrix is diagonally dominant, but often fail on general sparse matrices. We experiment with nonsymmetric permutations and scalings aimed at placing large entries on the diagonal in the context of preconditioning for general sparse matrices. We target highly indeenite,… (More)

We present a stable variant of the AINV factorized sparse approximate inverse algorithm which is applicable to any symmetric positive deenite matrix. The new preconditioner is breakdown-free and, when used in conjunction with the conjugate gradient method, results in a reliable parallel solver for highly ill-conditioned linear systems. We also investigate… (More)

We present a new approach for approximate updates of factorized nonsymmetric preconditioners for solving sequences of linear algebraic systems. This approach is algebraic and it is theoretically motivated. It generalizes diagonal updates introduced by Benzi and Bertaccini [3, 9]. It is shown experimentally that this approach can be very beneficial. For… (More)

The mixed hybrid nite element discretization of Darcy's law and continuity equation describing the potential uid ow problem in porous media leads to a symmetric indeenite linear system for the pressure and velocity vector components. As a method of solution the reduction to Schur complement systems based on successive block elimination is considered. The… (More)

The innuence of reorderings on the performance of factorized sparse approximate inverse preconditioners is considered. Some theoretical results on the eeect of orderings on the ll-in and decay behavior of the inverse factors of a sparse matrix are presented. It is shown experimentally that certain reorderings, like Minimum Degree and Nested Dissection, can… (More)

SUMMARY We describe a novel technique for computing a sparse incomplete factorization of a general symmetric positive deenite matrix A. The factorization is not based on the Cholesky algorithm (or Gaussian elimination), but on A{orthogonalization. Thus, the incomplete factorization always exists and can be computed without any diagonal modiication. When… (More)