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170
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
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Cited by 322 (15 self)
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The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, networks and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificiallygenerated matrices cannot meet, and is widely used by the sparse matrix algorithms community for the development and performance evaluation of sparse matrix algorithms. The collection includes software for accessing and managing the collection, from MATLAB, Fortran, and C.
Preconditioning techniques for large linear systems: A survey
 J. COMPUT. PHYS
, 2002
"... This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization i ..."
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Cited by 118 (5 self)
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This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions. Some of the challenges ahead are also discussed. An extensive bibliography completes the paper.
Solving unsymmetric sparse systems of linear equations with PARDISO
 Journal of Future Generation Computer Systems
, 2004
"... Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to ..."
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Cited by 110 (10 self)
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Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matrix entries on the diagonal. Complete block diagonal supernode pivoting allows dynamical interchanges of columns and rows during the factorization process. The level3 BLAS efficiency is retained and an advanced twolevel left–right looking scheduling scheme results in good speedup on SMP machines. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications. Key words: Computational sciences, numerical linear algebra, direct solver, unsymmetric linear systems
SuperLU DIST: A scalable distributedmemory sparse direct solver for unsymmetric linear systems
 ACM Trans. Mathematical Software
, 2003
"... We present the main algorithmic features in the software package SuperLU DIST, a distributedmemory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software’s parallel performance and sc ..."
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Cited by 105 (19 self)
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We present the main algorithmic features in the software package SuperLU DIST, a distributedmemory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software’s parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication patterns, which lets us exploit techniques used in parallel sparse Cholesky algorithms to better parallelize both LU decomposition and triangular solution on largescale distributed machines.
Hybrid scheduling for the parallel solution of linear systems
, 2004
"... apport de rechercheHybrid scheduling for the parallel solution of linear systems ..."
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Cited by 81 (11 self)
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apport de rechercheHybrid scheduling for the parallel solution of linear systems
A column preordering strategy for the unsymmetricpattern multifrontal method
 ACM Transactions on Mathematical Software
, 2004
"... A new method for sparse LU factorization is presented that combines a column preordering strategy with a rightlooking unsymmetricpattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on fillin and then refined during numerical factoriza ..."
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Cited by 67 (5 self)
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A new method for sparse LU factorization is presented that combines a column preordering strategy with a rightlooking unsymmetricpattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on fillin and then refined during numerical factorization (while preserving the bound). Pivot rows are selected to maintain numerical stability and to preserve sparsity. The method analyzes the matrix and automatically selects one of three preordering and pivoting strategies. The number of nonzeros in the LU factors computed by the method is typically less than or equal to those found by a wide range of unsymmetric sparse LU factorization methods, including leftlooking methods and prior multifrontal methods.
Recent Advances in Direct Methods for Solving Unsymmetric Sparse Systems of Linear Equations
, 2001
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The design and implementation of a new outofcore sparse Cholesky factorization method
 ACM Transactions on Mathematical Software
"... We describe a new outofcore sparse Cholesky factorization method. The new method uses the elimination tree to partition the matrix, an advanced subtreescheduling algorithm, and both rightlooking and leftlooking updates. The implementation of the new method is efficient and robust. On a 2 GHz per ..."
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Cited by 31 (4 self)
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We describe a new outofcore sparse Cholesky factorization method. The new method uses the elimination tree to partition the matrix, an advanced subtreescheduling algorithm, and both rightlooking and leftlooking updates. The implementation of the new method is efficient and robust. On a 2 GHz personal computer with 768 MB of main memory, the code can easily factor matrices with factors of up to 48 GB, usually at rates above 1 Gflop/s. For example, the code can factor AUDIKW, currenly the largest matrix in any matrix collection (factor size over 10 GB), in a little over an hour, and can factor a matrix whose graph is a 140by140by140 mesh in about 12 hours (factor size around 27 GB).
Analysis and comparison of two general sparse solvers for distributed memory computers
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2001
"... This paper provides a comprehensive study and comparison of two stateoftheart direct solvers for large sparse sets of linear equations on largescale distributedmemory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. We describe the main algo ..."
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Cited by 21 (7 self)
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This paper provides a comprehensive study and comparison of two stateoftheart direct solvers for large sparse sets of linear equations on largescale distributedmemory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. We describe the main algorithmic features of the two solvers and compare their performance characteristics with respect to uniprocessor speed, interprocessor communication, and memory requirements. For both solvers, preorderings for numerical stability and sparsity play an important role in achieving high parallel efficiency. We analyse the results with various ordering algorithms. Our performance analysis is based on data obtained from runs on a 512processor Cray T3E using a set of matrices from real applications. We also use regular 3D grid problems to study the scalability of the two solvers.
An Unsymmetrized Multifrontal LU Factorization
 SIAM Journal on Matrix Analysis and Applications
, 2000
"... A well known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A+A T and use it as a computational graph to drive the numerical factorization. This approach, although very efficient on a lar ..."
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Cited by 20 (4 self)
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A well known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A+A T and use it as a computational graph to drive the numerical factorization. This approach, although very efficient on a large range of unsymmetric matrices, does not capture the unsymmetric structure of the matrices. We introduce a new algorithm which detects and exploits the structural asymmetry of the submatrices involved during the processing of the elimination tree. We show that, with the new algorithm, significant gains both in memory and in time to perform the factorization can be obtained.