Miroslav Tuma

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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)
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 properties(More)
We present a variant of the AINV factorized sparse approximate inverse algorithm which is applicable to any symmetric positive definite matrix. The new preconditioner is breakdownfree and, when used in conjunction with the conjugate gradient method, results in a reliable solver for highly ill-conditioned linear systems. We also investigate an alternative(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)
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 LDLT 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 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)
In this paper we present a new incomplete factorization of a square matrix into triangular factors in which we get standard LU or LDLT factors (direct factors) and their inverses (inverse factors) at the same time. Algorithmically, we derive this method from the approach based on the Sherman-Morrison formula [18]. In contrast to the RIF algorithm [11], the(More)
This paper deals with solving sequences of nonsymmetric linear systems with a block structure arising from compressible flow problems. The systems are solved by a preconditioned iterative method. We attempt to improve the overall solution process by sharing a part of the computational effort throughout the sequence. Our approach is fully algebraic and it is(More)
This article focuses on the design and development of a new robust and efficient general-purpose incomplete Cholesky factorization package HSL_MI28, which is available within the HSL mathematical software library. It implements a limited memory approach that exploits ideas from the positive semidefinite Tismenetsky-Kaporin modification scheme and, through(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)