Journal Article10.1109/PROC.1977.10514
A survey of sparse matrix research
Iain S. Duff
- 01 Apr 1977
- Vol. 65, Iss: 4, pp 500-535
275
TL;DR: This paper surveys the state of the art in sparse matrix research in January 1976, and discusses the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms.
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Abstract: This paper surveys the state of the art in sparse matrix research in January 1976. Much of the survey deals with the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms. In the symmetric case, relevant terms from graph theory are defined. Band systems and matrices arising from the discretization of partial differential equations are treated as separate cases. Preordering techniques are surveyed with particular emphasis on partitioning (to block triangular form) and tearing (to bordered block triangular form). Methods for solving the least squares problem and for sparse linear programming are also reviewed. The sparse eigenproblem is discussed with particular reference to some fairly recent iterative methods. There is a short discussion of general iterative techniques, and reference is made to good standard texts in this field. Design considerations when implementing sparse matrix algorithms are examined and finally comments are made concerning the availability of codes in this area.
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Citations
The university of Florida sparse matrix collection
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TL;DR: The University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications, is described and a new multilevel coarsening scheme is proposed to facilitate this task.
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- 21 May 1990
TL;DR: The main features of a tool package for manipulating and working with sparse matrices, to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations, are presented.
Row-Action Methods for Huge and Sparse Systems and Their Applications
TL;DR: The main feature of row-action methods is that they are iterative procedures which, without making any changes to the original matrix A, use the rows of A, one row at a time as discussed by the authors.
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Wai-Hung Liu,Andrew H. Sherman +1 more
TL;DR: It is proved that for band elimination methods, the two orderings are equivalent and that, surprisingly, the reverse ordering is always at least as good as the original one when envelope elimination techniques are used.
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Computer implementation of the finite element method
John Alan George
- 01 Jan 1971
TL;DR: A detailed study of the implementation of finite element methods for solving two-dimensional elliptic partial differential equations shows that much of the manipulation of the basis functions necessary in the derivation of the approximation equations can be done semi-symbolically rather than numerically as is usually done.
A Simple Algorithm for Finding Maximal Network Flows and an Application to the Hitchcock Problem
L. R. Ford,D. R. Fulkerson +1 more
TL;DR: A very simple algorithm for finding a maximal flow and minimal cut in a transportation network is described and then applied to obtain an efficient computational routine for the Hitchcock distribution problem.
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•Proceedings Article
The automatic integration of stiff ordinary differential equations.
C. William Gear
- 01 Jan 1968
274
Notes on Linear Programming: Part XXIX A Simple Algorithm for Finding Maximal Network Flows and an Application to the Hitchcock Problem
L. R. Ford,D. R. Fulkerson +1 more
- 01 Jan 1955
TL;DR: In this article, a simple algorithm for finding a maximal flow and minimal cut in a transportation network is described; it is then applied to obtain an efficient computational routine for the Hitchcock distribution problem.