Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems
RAIRO - Operations Research - Recherche Opérationnelle, Volume 47 (2013) no. 1, pp. 59-71.

For solving linear complementarity problems LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting. But up to now, no paper has discussed the effect of preconditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and we use a class of preconditioners with generalized Accelerated Overrelaxation (GAOR) methods and analyze the convergence of these methods for LCP. Furthermore, Comparison between our methods and other non-preconditioned methods for the studied problem shows a remarkable agreement and reveals that our models are superior in point of view of convergence rate and computing efficiency. Besides, by choosing the appropriate parameters of these methods, we derive same results as the other iterative methods such as AOR, JOR, SOR etc. Finally the method is tested by some numerical experiments.

DOI: 10.1051/ro/2013027
Classification: 90C33, 65F10
Keywords: linear complementarity problems, preconditioning, iterative methods, H-matrix, obstacle problems
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     author = {Saberi Najafi, H. and Edalatpanah, S. A.},
     title = {Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {59--71},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {1},
     year = {2013},
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     zbl = {1276.90075},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2013027/}
}
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Saberi Najafi, H.; Edalatpanah, S. A. Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems. RAIRO - Operations Research - Recherche Opérationnelle, Volume 47 (2013) no. 1, pp. 59-71. doi : 10.1051/ro/2013027. http://archive.numdam.org/articles/10.1051/ro/2013027/

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