The algebraic eigenvalue problem
The algebraic eigenvalue problem
Inversion of Matrices by Partitioning
Journal of the ACM (JACM)
An Augmented Content-Addressed Memory Array for Implementation With Large-Scale Integration
Journal of the ACM (JACM)
Some Complexity Results for Matrix Computations on Parallel Processors
Journal of the ACM (JACM)
ACM Transactions on Programming Languages and Systems (TOPLAS)
ACM Transactions on Programming Languages and Systems (TOPLAS)
An efficient data structure for dynamic memory management
Journal of Systems and Software
Decentralized parallel algorithms for matrix computation
ISCA '78 Proceedings of the 5th annual symposium on Computer architecture
Some computer organizations and their effectiveness
IEEE Transactions on Computers
Batch Mode Active Learning for Networked Data
ACM Transactions on Intelligent Systems and Technology (TIST)
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Two general methods of matrix inversion, Gauss's algorithm and the method of bordering, are analyzed from the viewpoint of their adaptability for parallel computation. The analysis is not based on any specific type of parallel processor; its purpose is rather to see if parallel capabilities could be used effectively in matrix inversion.It is shown that both methods are indeed able to make effective use of parallel capability. With reasonable assumptions on the parallelism that is available, the speeds of the two methods are roughly comparable. The two methods, however, make use of different kinds of parallelism.To implement Gauss's algorithm we would like to have (a) parallel transfer capability for n numbers, if the matrix is n X n, (b) the capability for parallel multiplication of the accessed numbers by a common multiplier, and (c) parallel additive read-in capability. For the method of bordering, we need, primarily, the capability of forming the Euclidean inner product of two n-dimensional real vectors. The latter seems somewhat harder to implement, but, because it is an operation that is fundamental to linear algebra in general, it is one that might be made available for other purposes. If so, then the method of bordering becomes of interest.