منابع مشابه
Incremental incomplete LU factorizations with applications
This paper addresses the problem of computing preconditioners for solving linear systems of equations with a sequence of slowly varying matrices. This problem arises in many important applications. For example, a common situation in computational fluid dynamics, is when the equations change only slightly, possibly in some parts of the physical domain. In such situations it is wasteful to recomp...
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It is well known that any nonsingular M–matrix admits an LU factorization into M–matrices (with L and U lower and upper triangular respectively) and any singular M–matrix is permutation similar to an M–matrix which admits an LU factorization into M–matrices. Varga and Cai establish necessary and sufficient conditions for a singular M–matrix (without permutation) to allow an LU factorization wit...
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A singular matrix A may have more than one LU factorizations. In this work the set of all LU factorizations of A is explicitly described when the lower triangular matrix L is nonsingular. To this purpose, a canonical form of A under left multiplication by unit lower triangular matrices is introduced. This canonical form allows us to characterize the matrices that have an LU factorization and to...
متن کاملA Stability Analysis of Incomplete LU Factorizations
The combination of iterative methods with preconditionings based on incomplete LU factorizations constitutes an effective class of methods for solving the sparse linear systems arising from the discretization of elliptic partial differential equations. In this paper, we show that there are some settings in which the incomplete LU preconditioners are not effective, and we demonstrate that their ...
متن کاملPerturbation Theory for Factorizations of LU Type through Series Expansions
Componentand normwise perturbation bounds for the block LU factorization and block LDL∗ factorization of Hermitian matrices are presented. We also obtain, as a consequence, perturbation bounds for the usual pointwise LU, LDL∗, and Cholesky factorizations. Some of these latter bounds are already known, but others improve previous results. All the bounds presented are easily proved by using serie...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1979
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1979.101635