Abstract
Bai has recently presented a modulus-based matrix splitting iteration method, which is a powerful alternative for solving the large sparse linear complementarity problems. In this paper, we further present a two-step modulus-based matrix splitting iteration method, which consists of a forward and a backward sweep. Its convergence theory is proved when the system matrix is an H + -matrix. Moreover, for the two-step modulus-based relaxation iteration methods, more exact convergence domains are obtained without restriction on the Jacobi matrix associated with the system matrix, which improve the existing convergence theory. Numerical results show that the two-step modulus-based relaxation iteration methods are superior to the modulus-based relaxation iteration methods for solving the large sparse linear complementarity problems.
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Zhang, LL. Two-step modulus-based matrix splitting iteration method for linear complementarity problems. Numer Algor 57, 83–99 (2011). https://doi.org/10.1007/s11075-010-9416-7
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DOI: https://doi.org/10.1007/s11075-010-9416-7