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Abstract: . The multiple minimum degree (MMD) algorithm and its variants have enjoyed 20+ years of research and progress in generating fill-reducing orderings for sparse, symmetric positive definite matrices. Although conceptually simple, e#cient implementations of these algorithms are deceptively complex and highly specialized. In this case study, we present an object-oriented library that implements several recent minimum degreelike algorithms. We discuss how object-oriented design forces us to... (Update)
Context of citations to this paper: More
.... [80, 81, 83, 79, 82, 59, 58] PMLP [11, 12, 51] Di pack [17, 75] ISIS [2, 27] Sparspak or Sparspak90 [45] Oblio and Spindle [29, 28, 57] JAMA [68] Jampack [88, 25] BPKIT [21, 22, 23] Table 2: Object oriented linear algebra libraries. 3.1 Initial Analysis A matrix isatwo...
...matrix ordering algorithms to Fortran. Efforts to develop sparse matrix orderings with modern programming techniques include [2] and [3]. These were based on an object oriented, rather than generic, programming paradigm and although they were well programmed, the reported...
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BibTeX entry: (Update)
G. Kumfert and A. Pothen. An object-oriented collection of minimum degree algorithms: design, implementation, and experiences. In Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D. Caromel et al (eds.), pp. 95--106, Springer Verlag, 1998. http://citeseer.ist.psu.edu/kumfert98objectoriented.html More
@techreport{ kumfert99objectoriented,
author = "Gary Kumfert and Alex Pothen",
title = "An object-oriented collection of minimum degree algorithms: Design, implementation, and experiences",
number = "TR-99-1",
year = "1999",
url = "citeseer.ist.psu.edu/kumfert98objectoriented.html" }
Citations (may not include all citations):554 Design Patterns: Elements of Reusable Object-Oriented Softwa.. (context) - Gamma, Helm et al. - 1995
98 An approximate minimum degree ordering algorithm - Amestoy, Davis et al. - 1994 ACM
93 Computing the minimum fill-in is NP-complete (context) - Yannakakis - 1981
74 Modification of the minimum-degree algorithm by multiple eli.. (context) - Liu - 1985
30 Compressed graphs and the minimum degree algorithm (context) - Ashcraft - 1995 ACM
19 Node selection strategies for bottom-up sparse matrix orderi.. (context) - Rothberg, Eisenstat - 1998 ACM
12 The evolution of the minimum degree algorithm (context) - George, Liu - 1989
12 Ordering sparse matrices using approximate minimum local fil.. (context) - Rothberg - 1996
11 Performance of greedy ordering heuristics for sparse Cholesk.. - Ng, Raghavan - 1997
4 The use of planar graphs in Gaussian elimination (context) - Parter - 1961
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