Parallel Symbolic Factorization for Sparse LU with Static Pivoting
نویسندگان
چکیده
منابع مشابه
Parallel Symbolic Factorization for Sparse LU Factorization with Static Pivoting
In this paper we consider a direct method to solve a sparse unsymmetric system of linear equations Ax = b, which is the Gaussian elimination. This elimination consists in explicitly factoring the matrix A into the product of L and U , where L is a unit lower triangular matrix, and U is an upper triangular matrix, followed by solving LUx = b one factor at a time. One of the main characteristics ...
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This paper presents the design and implementation of a memory scalable parallel symbolic factorization algorithm for general sparse unsymmetric matrices. Our parallel algorithm uses a graph partitioning approach, applied to the graph of |A|+ |A| , to partition the matrix in such a way that is good for sparsity preservation as well as for parallel factorization. The partitioning yields a so-call...
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In this paper we present several improvements of widely used parallel LU factorization methods on sparse matrices. First we introduce the LU elimination forest and then we characterize the L, U factors in terms of their corresponding LU elimination forest. This characterization can be used as a compact storage scheme of the matrix as well as of the task dependence graph. To improve the use of B...
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Gaussian elimination based sparse LU factorization with partial pivoting is important to many scientiic applications, but it is still an open problem to develop a high performance sparse LU code on distributed memory machines. The main diiculty is that partial pivoting operations make structures of L and U factors unpredictable beforehand. This paper presents an approach called S for paralleliz...
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We consider the problem of structure prediction for sparse LU factorization with partial pivoting. In this context, it is well known that the column elimination tree plays an important role for matrices satisfying an irreducibility condition, called the strong Hall property. Our primary goal in this paper is to address the structure prediction problem for matrices satisfying a weaker assumption...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2007
ISSN: 1064-8275,1095-7197
DOI: 10.1137/050638102