منابع مشابه
Crout Versions of ILU for General Sparse Matrices
This paper presents an e cient implementation of incomplete LU (ILU) factorizations that are derived from the Crout version of Gaussian elimination (GE). At step k of the elimination, the k-th row of U and the k-th column of L are computed using previously computed rows of U and columns of L. The data structure and implementation borrow from already known techniques used in developing both spar...
متن کاملCrout Versions of the Ilu Factorization with Pivoting for Sparse Symmetric Matrices
The Crout variant of ILU preconditioner (ILUC) developed recently has been shown to have a number of advantages over ILUT, the conventional row-based ILU preconditioner [14]. This paper explores pivoting strategies for sparse symmetric matrices to improve the robustness of ILUC. This paper shows how to integrate two symmetry-preserving pivoting strategies, the diagonal pivoting and the Bunch-Ka...
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Dimensionality reduction has become a critical tool for quickly solving massive matrix problems. Especially in modern data analysis and machine learning applications, an overabundance of data features or examples can make it impossible to apply standard algorithms efficiently. To address this issue, it is often possible to distill data to a much smaller set of informative features or examples, ...
متن کاملAn approximate cyclic reduction multilevel preconditioner for general sparse matrices
We discuss an iterative method for solving large sparse systems of equations. A hybrid method is introduced which uses ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by using maximal independent sets for graph coarsening. For Schur complement approximation on coarser graphs an incomplet...
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The problem of sparse matrix bandwidth reduction is addressed and solved with two approaches suitable for both symmetric and non-symmetric matrices. The former is a constructive method, the latter is an application of a metaheuristic scheme. This heuristic algorithm has been implemented on parallel machines. Both approaches are compared with previous methods in the literature (suited only for s...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 1969
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/12.2.158