The algebraic eigenvalue problem
The algebraic eigenvalue problem
Tree machines and divide-and-conquer algorithms
CONPAR '81 Proceedings of the Conference on Analysing Problem Classes and Programming for Parallel Computing
Algorithmic aspects of vertex elimination
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
A Data Structure for Parallel L/U Decomposition
IEEE Transactions on Computers
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In this paper it is investigated which pivots may be processed simultaneously when solving a set of linear equations. It is shown that for dense sets of equations all the pivots must necessarily be processed one at a time; only if the set is sufficiently sparse, some pivots may be processed simultaneously. We present parallel pivoting algorithms for MIMD computers with sufficiently many processors and a common memory. Moreover we present algorithms for MIMD computers with an arbitrary, but fixed number of processors. For both types of computers algorithms embodying an ordering strategy are given.