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| ASCII Text | x | ||
| J.A.G. Jess, H.G.M. Kees, "A Data Structure for Parallel L/U Decomposition," IEEE Transactions on Computers, vol. 31, no. 3, pp. 231-239, March, 1982. | |||
| BibTex | x | ||
| @article{ 10.1109/TC.1982.1675979, author = {J.A.G. Jess and H.G.M. Kees}, title = {A Data Structure for Parallel L/U Decomposition}, journal ={IEEE Transactions on Computers}, volume = {31}, number = {3}, issn = {0018-9340}, year = {1982}, pages = {231-239}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1982.1675979}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - A Data Structure for Parallel L/U Decomposition IS - 3 SN - 0018-9340 SP231 EP239 EPD - 231-239 A1 - J.A.G. Jess, A1 - H.G.M. Kees, PY - 1982 KW - triangulated graph KW - Elimination-tree KW - L/U decomposition KW - parallel processing KW - schedule KW - sparse matrix pivoting KW - task graph KW - tearing VL - 31 JA - IEEE Transactions on Computers ER - | |||
Some new results are presented concerning the pivoting of large systems of linear equations with respect to parallel processing techniques. It will be assumed that the processing of a pivot takes one time slot. The pivoting problem is studied by means of an associated graph model. Given a triangulated graph a set of label classes is established. Class k contains all pivots which may be processed in parallel during the kth time slot. The label classes are used to establish the elimination-tree (e-tree). The e-tree is a spanning tree for the given graph. The critical path in the e-tree indicates the minimum number of time slots necessary to complete the L/U-decomposition. Furthermore, the earliest and latest admissible time slot for the processing of every pivot may be derived, such that the critical path is not affected. The e-tree can be seen as a data structure to guide parallel processing based on sparsity.
Index Terms:
triangulated graph, Elimination-tree, L/U decomposition, parallel processing, schedule, sparse matrix pivoting, task graph, tearing
Citation:
J.A.G. Jess, H.G.M. Kees, "A Data Structure for Parallel L/U Decomposition," IEEE Transactions on Computers, vol. 31, no. 3, pp. 231-239, March 1982, doi:10.1109/TC.1982.1675979
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