Showing papers on "Sparse approximation published in 1974"
369 citations
TL;DR: The computational complexity of partitioning sparse matrices is developed graph-theoretically and the results are used to study tearing and modification, and to show that single-element tearing of symmetric systems is rarely advantageous when the torn system is solved by elimination.
51 citations
TL;DR: Several strategies for pivot selection in Givens reduction to upper triangular form and for row ordering within major steps of the reduction are compared on the grounds of how well they preserve sparsity.
Abstract: Several strategies for pivot selection in Givens reduction to upper triangular form and for row ordering within major steps of the reduction are compared on the grounds of how well they preserve sparsity. Recommendations are made based principally on the results of runs on test problems. The use of Givens similarity transformations in reducing a sparse matrix to Hessenberg form is similarly examined and finally some conclusions are drawn as to the advisability of using Givens reduction methods on sparse systems.
34 citations
14 citations
12 citations
TL;DR: Practical rules for searching for the most probable optimum pivot as well as their implementation and computation results are presented for both the deterministic and probabilistic algorithms.
Abstract: During each step of Gaussian elimination (GE), if ties occur for a minimum fill-in algorithm, an additional criterion is required to search for the most probable optimum pivot. Theoretical justifications for this criterion are developed. Practical rules for searching for these pivots as well as their implementation and computation results are presented for both the deterministic and probabilistic algorithms.
9 citations
TL;DR: Methods of hashing the subscripts of a matrix to give a suitable address in the scatter storage table are investigated and different types of sparse matrices are considered.
Abstract: It has been suggested that key transformation techniques might be a very effective way of manipulating sparse matrices particularly if the operations on the matrix access the elements in an unsystematic way. The purpose of the present paper is to investigate methods of hashing the subscripts of a matrix to give a suitable address in the scatter storage table. Various different types of sparse matrices are considered.
7 citations