Modification of the minimum-degree algorithm by multiple elimination

Liu, Joseph W. H.

doi:10.1145/214392.214398

Cited by 270 publications

(112 citation statements)

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“…Many popular LP solvers [17,18] call a software package [33] which uses some linear algebra specifically developed for the sparse Cholesky decomposition [34]. However, MATLAB does not yet have this function to call.…”

Section: Linear Algebra For Sparse Cholesky Matrixmentioning

confidence: 99%

CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Yang¹

2016

Numer Algor

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Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the proposed arc-search infeasible interior-point algorithm is a more efficient algorithm than Mehrotra's algorithm.

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Section: Linear Algebra For Sparse Cholesky Matrixmentioning

confidence: 99%

CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Yang¹

2016

Numer Algor

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“…In order to minimize fill-in the minimum degree algorithm (MD) and its variants [16,27] remove the nodes with smallest valence first from the elimination graph, since this causes the least number of additional pairwise connections. Many efficiency optimizations of this basic method exist, the most prominent of which is the super-nodal approach: instead of removing eliminated nodes from the graph, neighboring eliminated nodes are clustered to so-called super-nodes, allowing for more efficient graph updates.…”

Section: Sparse Direct Solversmentioning

confidence: 99%

Efficient Linear System Solvers for Mesh Processing

Botsch

Bommes

Kobbelt

2005

Mathematics of Surfaces XI

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Abstract. The use of polygonal mesh representations for freeform geometry enables the formulation of many important geometry processing tasks as the solution of one or several linear systems. As a consequence, the key ingredient for efficient algorithms is a fast procedure to solve linear systems. A large class of standard problems can further be shown to lead more specifically to sparse, symmetric, and positive definite systems, that allow for a numerically robust and efficient solution. In this paper we discuss and evaluate the use of sparse direct solvers for such kind of systems in geometry processing applications, since in our experiments they turned out to be superior even to highly optimized multigrid methods, but at the same time were considerably easier to use and implement. Although the methods we present are well known in the field of high performance computing, we observed that they are in practice surprisingly rarely applied to geometry processing problems.

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“…This strategy was introduced by Liu [5]. The scheme used for symbolic factorization is partly described by Liu [6] and Gilbert, Ng, and Peyton [3].…”

Section: Linear Algebramentioning

confidence: 99%