Numer Algor DOI 10.1007/s11075-014-9824-1 ORIGINAL PAPER On the choice of parameters in MAOR type splitting methods for the linear complementarity problem Lj. Cvetkovi´ c · A. Hadjidimos · V. Kosti´ c Received: 25 July 2013 / Accepted: 2 January 2014 © Springer Science+Business Media New York 2014 Abstract In the present work we consider the iterative solution of the Linear Com- plementarity Problem (LCP), with a nonsingular H + coefficient matrix A, by using all modulus-based matrix splitting iterative methods that have been around for the last couple of years. A deeper analysis shows that the iterative solution of the LCP by the modified Accelerated Overrelaxation (MAOR) iterative method is the “best”, in a sense made precise in the text, among all those that have been proposed so far regarding the following three issues: i) The positive diagonal matrix-parameter  ≥ diag(A) involved in the method is  = diag(A), ii) The known convergence intervals for the two AOR parameters, α and β, are the widest possible, and iii) The “best” possible MAOR iterative method is the modified Gauss-Seidel one. Keywords Linear complementarity problem (LCP) · M−matrices · H + −matrices · Modulus-based splitting iterative methods · Multisplitting methods · Modified AOR iterative methods Mathematics Subject Classifications (2010) Primary 65F10 L. Cvetkovi´ c · V. Kosti´ c Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Republic of Serbia L. Cvetkovi´ c e-mail: lila@dmi.uns.ac.rs V. Kosti´ c e-mail: vkostic@dmi.uns.ac.rs A. Hadjidimos () Department of Electrical and Computer Engineering, University of Thessaly, GR-382 21 Volos, Greece e-mail: hadjidim@inf.uth.gr