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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 84
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 91
Alternating Two-Stage Methods for the Parallel Solution of Linear Systems H. Migallón1, V. Migallón2 and J. Penadés2
1Department of Physics and Computer Architectures, University Miguel Hernández, Elche, Alicante, Spain
Full Bibliographic Reference for this paper
, "Alternating Two-Stage Methods for the Parallel Solution of Linear Systems", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Fifth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 91, 2006. doi:10.4203/ccp.84.91
Keywords: alternating two-stage methods, parallel algorithms, linear systems, block methods, Markov chains.
Summary
We consider the
![]() where A is a matrix such that b is in ![]() ![]() where ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() The alternating two-stage method can be written as follows, for ![]() ![]()
In a similar manner as the two-stage methods, we say that an alternating two-stage method is stationary when
These methods are suitable for parallel computation. These alternating two-stage methods have been implemented on two different parallel operating systems. One of them is a distributed multiprocessor IBM RS/6000 SP with 8 nodes. These nodes are 120 MHz Power2 Super Chip and are connected through a high performance switch with latency time of 40 microseconds and a bandwidth of 110 Mbytes per second. The second system used is an Ethernet network of six Pentiums IV running Linux and connected through a switch with a bandwidth of 1 Gbit per second. The parallel environment has been managed using the MPI library of parallel routines. The algorithms have been applied to the solution of singular linear systems arising from Markov chain modeling. These experiments demonstrate that the parallel implementation of these methods can solve singular systems of linear equations in substantially less time that the sequential counterparts. Furthermore, different versions of these methods and implementation strategies are explored and their relative merit discussed. References
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