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
Timothy A. Davis,Yifan Hu +1 more
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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SPARSKIT: A basic tool kit for sparse matrix computations
Youcef Saad
- 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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References
Analysis of the Diagonal Pivoting Method
TL;DR: In this paper, a backward error analysis of the diagonal pivoting method for solving symmetric systems of linear equations is presented, which shows that the elements of the associated error matrix can be bounded in time.
73
Application of the simultaneous iteration method to undamped vibration problems
Alan Jennings,D. R. L. Orr +1 more
TL;DR: In this paper, the simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems, and a method of allowing for body freedom is given and some numerical tests are discussed.
72
Finite-element structural analysis
T. Furuike,J. C. Long +1 more
- 01 Jun 1977
TL;DR: In this article, critical loading conditions for critical values of reactions, applied loads, deflections, stresses, internal loads and internal loads are determined for a computer program in one of specified three-part format.
72