Computational experience with the octahedral algorithm and related results. Technical Report SOL 83-8
Technical Report
·
OSTI ID:5905443
This paper investigates the computational efficiency of the octahedral algorithm of Wright. The algorithm avoids a subdivision of the full product space R/sup n/ x (0, 1); in particular, only 2n artificial vertices are required. The algorithm can be interpreted as a variable dimension algorithm in which simplices in R/sup n/ of varying dimension are traversed. There are 2/sup n/ directions (rays) where efficient one-dimensional pivots are permitted. These and other features make the octahedral algorithm a promising new method for computing fixed points. The algorithm can be interpreted as dual to the cubical algorithm of Van der Laan and Talman (1981), see Wright (1981). Their cubical algorithm which has 2n-rays is based on C/sup n/, the n-dimensional unit cube, which is dual to O/sup n/. A concise description is presented of the octahedral algorithm and the replacement (pivot) rules which are necessary to implement the algorithm are given. Computational results are given and shortest paths through the octahedral subdivision are derived.
- Research Organization:
- Stanford Univ., CA (USA). Systems Optimization Lab.
- DOE Contract Number:
- AT03-76ER72018
- OSTI ID:
- 5905443
- Report Number(s):
- DOE/ER/72018-T10; ON: DE83015834
- Country of Publication:
- United States
- Language:
- English
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