A Novel Parallel Algorithm for Gaussian Elimination of Sparse Unsymmetric Matrices
نویسنده
چکیده
We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to sequential execution. We present a sample MPI implementation of a program computing the rank of a sparse integer matrix using the proposed algorithm. Some preliminary performance measurements are presented and discussed, and the performance of the algorithm is compared to corresponding state-ofthe-art algorithms for floating-point and integer matrices.
منابع مشابه
Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matrices
We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations. We have modified a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures. We give an efficient algorithm to compute a near-minimal data-dependency graph for unsymmetric multifront...
متن کاملHypergraph-Based Unsymmetric Nested Dissection Ordering for Sparse LU Factorization
In this paper we present HUND, a hypergraph-based unsymmetric nested dissection ordering algorithm for reducing the fill-in incurred during Gaussian elimination. HUND has several important properties. It takes a global perspective of the entire matrix, as opposed to local heuristics. It takes into account the assymetry of the input matrix by using a hypergraph to represent its structure. It is ...
متن کاملUnsymmetric-pattern Multifrontal Methods for Parallel Sparse Lu Factorization
Sparse matrix factorization algorithms are typically characterized by irregular memory access patterns that limit their performance on parallel-vector supercomputers. For symmetric problems, methods such as the multifrontal method replace irregular operations with dense matrix kernels. However, no e cient method based primarily on dense matrix kernels exists for matrices whose pattern is very u...
متن کاملParallel 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 ...
متن کاملA Supernodal Out-of-Core Sparse Gaussian-Elimination Method
We present an out-of-core sparse direct solver for unsymmetric linear systems. The solver factors the coefficient matrix A into A = PLU using Gaussian elimination with partial pivoting. It assumes that A fits within main memory, but it stores the L and U factors on disk (that is, in files). Experimental results indicate that on small to moderately-large matrices (whose factors fit or almost fit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011