Matrix Inversion Using Parallel ProcessingMatrix Inversion Using Parallel Processing

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 Author Pease, Marshall C. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1967 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract 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 $\textit{n}$ numbers, if the matrix is $\textit{n}$ X $\textit{n},$ (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 $\textit{n}-dimensional$ 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. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1967-10-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 14 Issue Number 4 Page Count 8 Starting Page 757 Ending Page 764

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Source: ACM Digital Library