Abstract
We consider the convergence theory of the Successive Overrelaxation (SOR) iterative method for the solution of linear systems Ax = b, when the matrix A has block a p × p partitioned p-cyclic form. Our purpose is to extend much of the p-cyclic SOR theory for nonsingular A to consistent singular systems and to apply the results to the solution of large scale systems arising, e.g., in queueing network problems in Markov analysis. Markov chains and queueing models lead to structured singular linear systems and are playing an increasing role in the understanding of complex phenomena arising in computer, communication and transportation systems.
For certain important classes of singular problems, we develop a convergence theory for p-cyclic SOR, and show how to repartition for optimal convergence. Recent results by Kontovasilis, Plemmons and Stewart on the new concept of convergence of SOR in an extended sense are further analyzed and applied to the solution of periodic Markov chains.
Research supported in part by NSF grant CCR-86-19817 and by the US Air Force under grant no. AFOSR-88-10243.
Research supported by the US Air Force under grant no. AFOSR-91-0163.
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© 1993 Springer-Verlag New York, Inc.
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Hadjidimos, A., Plemmons, R.J. (1993). Analysis of P-Cyclic Iterations for Markov Chains. In: Meyer, C.D., Plemmons, R.J. (eds) Linear Algebra, Markov Chains, and Queueing Models. The IMA Volumes in Mathematics and its Applications, vol 48. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8351-2_8
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