Solving Large-Scale Sparse Linear Complementarity Problems Using a Relaxed Shifted Matrix-Splitting Modulus-Based Iteration Method
Abstract
A relaxed shifted matrix-splitting modulus-based iteration method is proposed for solving large-scale sparse linear complementarity problems. The method extends the classical modulus-based matrix-splitting framework by introducing two shift parameters into the matrix splitting while preserving the original coefficient matrix. Different choices of the splitting lead to shifted Jacobi, Gauss-Seidel, SOR, and AOR-type schemes. Sufficient convergence conditions are established for P-matrices and H+-matrices. For structured sparse matrices, practical AOR-type conditions and explicit admissible intervals for the shift parameters are also derived. These intervals are used together with a grid-search procedure to select efficient parameter pairs. Numerical experiments on four large-scale sparse test problems, including a quasi-variational inequality model, show that the proposed method is competitive with several existing modulus-based and projected methods. A direct comparison with the two-parameter MAOR method further illustrates the effect of the proposed shifted splitting.
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BibTeX
@misc{sengar2026solving,
title = {{Solving Large-Scale Sparse Linear Complementarity Problems Using a Relaxed Shifted Matrix-Splitting Modulus-Based Iteration Method}},
author = {Abhishek Kumar Singh Sengar and Bharat Kumar and Deepmala},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11949},
eprint = {2609.11949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11949},
}
RIS
TY - UNPB
TI - Solving Large-Scale Sparse Linear Complementarity Problems Using a Relaxed Shifted Matrix-Splitting Modulus-Based Iteration Method
AU - Abhishek Kumar Singh Sengar
AU - Bharat Kumar
AU - Deepmala
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.11949
UR - https://arxiv.org/abs/2609.11949
AB - A relaxed shifted matrix-splitting modulus-based iteration method is proposed for solving large-scale sparse linear complementarity problems. The method extends the classical modulus-based matrix-splitting framework by introducing two shift parameters into the matrix splitting while preserving the original coefficient matrix. Different choices of the splitting lead to shifted Jacobi, Gauss-Seidel, SOR, and AOR-type schemes. Sufficient convergence conditions are established for P-matrices and H_+-matrices. For structured sparse matrices, practical AOR-type conditions and explicit admissible intervals for the shift parameters are also derived. These intervals are used together with a grid-search procedure to select efficient parameter pairs. Numerical experiments on four large-scale sparse test problems, including a quasi-variational inequality model, show that the proposed method is competitive with several existing modulus-based and projected methods. A direct comparison with the two-parameter MAOR method further illustrates the effect of the proposed shifted splitting.
ER -