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268
A review of algebraic multigrid
, 2001
"... Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had to b ..."
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Cited by 347 (11 self)
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discretized on unstructured meshes, both in 2D and 3D. Since AMG does not make use of any geometric information, it is a “plugin ” solver which can even be applied to problems without any geometric background, provided that the
CommunicationAvoiding LinearAlgebraic Primitives for Graph Analytics
"... Graph algorithms typically have very low computational intensities, hence their execution times are bounded by their communication requirements. In addition to improving the running time drastically, reducing communication will also help improve the energy consumption of graph algorithms. Many of th ..."
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more available memory are the socalled 3D algorithms, yet the existing software for graph analytics is either 1D or 2D. In this talk, I will describe two new communicationavoiding kernels for graph computations, discuss how they can be integrated into an existing library like the Combinatorial BLAS
Linear Algebra Operators for GPU Implementation of Numerical Algorithms
 ACM Transactions on Graphics
, 2003
"... In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for ..."
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Cited by 324 (9 self)
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direct solvers for sparse matrices, and by applying these solvers to multidimensional finite difference equations, i.e. the 2D wave equation and the incompressible NavierStokes equations.
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 145 (18 self)
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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
Direct solvers for sparse matrices
 http://crd.lbl.gov/~xiaoye/SuperLU/ SparseDirectSurvey.pdf
"... Direct solvers for sparse matrices involve much more complicated algorithms than for dense matrices. The main complication is due to the need for efficient handling the fillin in the factors L and U. A typical sparse solver consists of four distinct steps as opposed to two in the dense case: 1. An ..."
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Cited by 4 (0 self)
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Direct solvers for sparse matrices involve much more complicated algorithms than for dense matrices. The main complication is due to the need for efficient handling the fillin in the factors L and U. A typical sparse solver consists of four distinct steps as opposed to two in the dense case: 1
Sparsifying Synchronization for HighPerformance SharedMemory Sparse Triangular Solver
"... Abstract. The last decade has seen rapid growth of singlechip multiprocessors (CMPs), which have been leveraging Moore’s law to deliver high concurrency via increases in the number of cores and vector width. Modern CMPs execute from several hundreds to several thousands concurrent operations per ..."
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Cited by 2 (0 self)
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such kernel and is the focus of this paper. It is widely used in several types of sparse linear solvers, and it is commonly considered challenging to parallelize and scale even on a moderate number of cores. This challenge is due to the fact that triangular solver typically has limited tasklevel parallelism
Performance of a fully parallel sparse solver
 International Journal of Supercomputer Applications and High Performance Computing Applications
, 1997
"... The performance of a fully parallel direct solver for large sparsesymmetric positive definite systems of linear equations is demonstrated. The solver is designed for distributedmemory, messagepassing parallel computer systems. All phases of the computation, including symbolic processing as well ..."
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Cited by 21 (4 self)
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The performance of a fully parallel direct solver for large sparsesymmetric positive definite systems of linear equations is demonstrated. The solver is designed for distributedmemory, messagepassing parallel computer systems. All phases of the computation, including symbolic processing as well
A latency tolerant hybrid sparse solver using . . .
 NUMER. LINEAR ALGEBRA APPL.
, 2003
"... Consider the solution of large sparse symmetric positive definite linear systems using the preconditioned conjugate gradient method. On sequential architectures, incomplete Cholesky factorizations provide effective preconditioning for systems from a variety of application domains, some of which may ..."
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Cited by 6 (4 self)
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to the large latency of interprocessor communication. We propose a new approach to overcome this performance bottleneck by coupling incomplete factorization with a selective inversion scheme to replace triangular solutions by scalable matrix–vector multiplications. We discuss our algorithm, analyze its
Factors Impacting Performance of Multithreaded Sparse Triangular Solve
"... Abstract. As computational science applications grow more parallel with multicore supercomputers having hundreds of thousands of computational cores, it will become increasingly difficult for solvers to scale. Our approach is to use hybrid MPI/threaded numerical algorithms to solve these systems in ..."
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Cited by 5 (0 self)
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triangular solver, an important kernel for preconditioning. We analyze three factors that affect the parallel performance of this threaded kernel and obtain good scalability on the multicore nodes for a range of matrix sizes.
A LargeGrain Parallel Sparse System Solver
 In Proc. Fourth SIAM Conf. on Parallel Proc. for Scient. Comp
, 1989
"... . The efficiency of solving sparse linear systems on parallel processors and more complex multicluster architectures such as Cedar is greatly enhanced if relatively large grain computational tasks can be assigned to each cluster or processor. The ordering of a system into a bordered block upper tria ..."
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Cited by 8 (1 self)
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triangular form facilitates a reasonable largegrain partitioning. A new algorithm which produces this form for unsymmetric sparse linear systems is considered and the associated factorization algorithm is presented. Computational results are presented for the Cedar multiprocessor. Several techniques have
Results 1  10
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