The evolution of the minimum degree ordering algorithm

George, Alan; Liu, J. W.H.

doi:10.2172/5686483

Cited by 76 publications

(105 citation statements)

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“…For some cases, some reordering technique like the Multiple Minimal Degree (MMD) ordering [12], may help reduce the number of levels so as to increase parallelism. However, in general, the performance of solving a sparse triangular system on GPUs is lower than that on CPUs, especially for triangular systems obtained from high-fill-in factorizations which usually have a large number of levels.…”

Section: Gpu Implementationmentioning

confidence: 99%

GPU-accelerated preconditioned iterative linear solvers

2012

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This work is an overview of our preliminary experience in developing a high-performance iterative linear solver accelerated by GPU coprocessors. Our goal is to illustrate the advantages and difficulties encountered when deploying GPU technology to perform sparse linear algebra computations. Techniques for speeding up sparse matrix-vector product (SpMV) kernels and finding suitable preconditioning methods are discussed. Our experiments with an NVIDIA TESLA M2070 show that for unstructured matrices SpMV kernels can be up to 8 times faster on the GPU than the Intel MKL on the host Intel Xeon X5675 Processor. Overall performance of the GPU-accelerated Incomplete Cholesky (IC) factorization preconditioned CG method can outperform its CPU counterpart by a smaller factor, up to 3, and GPU-accelerated The incomplete LU (ILU) factorization preconditioned GMRES method can achieve a speed-up nearing 4. However, with better suited preconditioning techniques for GPUs, this performance can be further improved.

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Section: Gpu Implementationmentioning

confidence: 99%

GPU-accelerated preconditioned iterative linear solvers

2012

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“…This preserves the original combination of equations into groups. In addition, the amount of data in the adjacency graph for the FE model's nodes is much less than that in the adjacency graph for the sparse matrix's structure, therefore the well-known reordering algorithms [7,8,17,18] work much faster here.…”

Section: Decomposition Of Sparse Matrix a Into Dense Rectangular Submmentioning

confidence: 99%

PARFES: A method for solving finite element linear equations on multi-core computers

Fialko

2010

Advances in Engineering Software

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“…Practical implementations of sparse Cholesky factorization therefore rely on heuristics to compute some ordering with an acceptable number of fill-in. Examples of such heuristic approaches include minimum degree [13] and nested dissection [14].…”

Section: Sparse Cholesky Factorizationmentioning

confidence: 99%

Interactively exploring elimination orderings in symbolic sparse Cholesky factorization

Lülfesmann

Leßenich

Bücker

2010

Procedia Computer Science

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When large sparse symmetric systems of linear equations are solved by the Cholesky factorization, nonzero elements can be generated at positions where the original matrix contains zero elements. This phenomenon is called fill-in and it is often crucial in large-scale problems. The symbolic Cholesky factorization solely takes into account the nonzero structure of a sparse matrix to determine the nonzero structure of its Cholesky factor. Sequences of elimination graphs are typically used to model this combinatorial problem. We propose an interactive educational module to visualize and explore the symbolic Cholesky factorization in terms of both elimination graphs and matrix representation. We describe the design and implementation of this interactive module that is intended to be used in a face-to-face learning environment.

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The evolution of the minimum degree ordering algorithm

Cited by 76 publications

References 0 publications

GPU-accelerated preconditioned iterative linear solvers

GPU-accelerated preconditioned iterative linear solvers

PARFES: A method for solving finite element linear equations on multi-core computers

Interactively exploring elimination orderings in symbolic sparse Cholesky factorization

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