NDLI: Optimal n-line Successive Over Relaxation

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Optimal n-line Successive Over Relaxation

Content Provider	ACM Digital Library
Author	Johnson, Olin G.
Abstract	It is well known in numerical analysis that the computation per iteration in n-line S.O.R. for solving elliptic difference equations increases linearly with n whereas the asymptotic rate of convergence increases only with @@@@n3,4. Hence, it has been said 5 there is no reason to use n-line S.O.R. where n is greater than ten, say. In a modern computing environment, however, the situation is not so simple for problems which are larger than core size. Most computers today offer simultaneous “read-write-compute”, hence the time per iteration cannot be identified with the computation per iteration. A more reasonable optimization technique would be to find the minimum over n of the maximum of compute time, input time, and output time. However, even this technique suffers from the fact that there are trade-offs between these three which can be taken into account. In this paper, we attempt a quantitative determination of optimal n-line S.O.R. in this more complicated setting. The function to be minimized is, of course, machine dependent. It will vary with compute speed, I/O speed, n, and the programming strategy. In section two, we consider a restricted n-line S.O.R. problem in which there is no trade-off between computation and input-output. That is, programming strategy is omitted. In section three, we identify the trade-offs which are allowable, and in sections four and five we consider the problem with programming strategy. Finally, in section six, we apply the results to representative machine configurations.
Starting Page	173
Ending Page	177
Page Count	5
File Format	PDF
DOI	10.1145/800195.805929
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1969-08-26
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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