Improved convergence theorems of the two-step modulus-based matrix splitting and synchronous multisplitting iteration methods for solving linear complementarity problems

References

• Murty KG. Linear complementarity, linear and nonlinear programming. Berlin: Heldermann Verlag; 1988.
   Google Scholar
• Cottle RW, Pang J-S, Stone RE. The linear complementarity problem. SanDiego: Academic; 1992.
   Google Scholar
• van Bokhoven WMG. Piecewise-linear modelling and analysis. Eindhoven: Proefschrift; 1981.
   Google Scholar
• Bai Z-Z. Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer Linear Algebra Appl. 2010;17:917–933.
   Web of Science ®Google Scholar
• Zhang L-L. Two-step modulus-based matrix splitting iteration for linear complementarity problems. Numer Alg. 2011;57:83–99.
   Web of Science ®Google Scholar
• Bai Z-Z, Zhang L-L. Modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Numer Linear Algebra Appl. 2013;20:425–439.
   Web of Science ®Google Scholar
• Zhang L-L. Two-step modulus-based synchronous multisplitting iteration methods for linear complementarity problems. J Comput Math. 2015;33:100–112.
   Web of Science ®Google Scholar
• Li W. A general modulus-based matrix splitting method for linear complementarity problems of H-matrices. Appl Math Lett. 2013;26:1159–1164.
   Web of Science ®Google Scholar
• Bai Z-Z, Zhang L-L. Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems. Numer Alg. 2013;62:59–77.
   Web of Science ®Google Scholar
• Zheng N, Yin J-F. Accelerated modulus-based matrix splitting iteration methods for linear complementarity problems. Numer Alg. 2013;64:245–262.
   Web of Science ®Google Scholar
• Zhang L-L, Ren Z-R. Improved convergence theorems of modulus-based matrix splitting iteration methods for linear complementarity problems. Appl Math Lett. 2013;26:638–642.
   Web of Science ®Google Scholar
• Cvetković Lj. Kostić V. A note on the convergence of the MSMAOR method for linear complementarity problems. Numer. Linear Algebra Appl. 2014;21:534–539.
   Web of Science ®Google Scholar
• Zhang L-L. Two-stage multisplitting iteration methods using modulus-based matrix splitting as inner iteration for linear complementarity problems. J Optim Theory Appl. 2014;160:189–203.
   Web of Science ®Google Scholar
• Cvetković Lj, Hadjidimos A, Kostić V. On the choice of parameters in MAOR type splitting methods for the linear complementarity problem. Numer Alg. 2014;64:793–806.
   Google Scholar
• Zhang L-T, Li J-L. The weaker convergence of modulus-based synchronous multisplitting multi-parameters methods for linear complementarity problems. Comput Math Appl. 2014;67(10):1954–1959.
   Web of Science ®Google Scholar
• Zhang L-L, Zhang Y-P, Ren Z-R. New convergence proofs of modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Linear Algebra Appl. 2015;481:83–93.
   Web of Science ®Google Scholar
• Liu S-M, Zheng H, Li W. A general accelerated modulus-based matrix splitting iteration method for solving linear complementarity problems. Calcolo. 2016;53:189–199.
   Web of Science ®Google Scholar
• Li W, Zheng H. A preconditioned modulus-based iteration method for solving linear complementarity problems of H-matrices. Linear Multilinear Algebra. 2016;64:1390–1403.
   Web of Science ®Google Scholar
• Cvetković Lj, Kostić V, Šanca E. A wider convergence area for the MSTMAOR iteration methods for LCP. Numer Alg. 2016;71:77–88.
   Web of Science ®Google Scholar
• Zheng H, Li W, Vong S. A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems. Numer. Algorithms. 2017;74:137–152.
   Web of Science ®Google Scholar
• Bai Z-Z, Zhang L-L. Modulus-based multigrid methods for linear complementarity problems. Numer. Linear Algebra Appl. 2017;24(e2105):1–15.
   Google Scholar
• Bai Z-Z, Buccini A, Hayami K, et al. Modulus-based iterative methods for constrained Tikhonov regularization. J Comput Appl Math. 2017;319:1–13.
   Web of Science ®Google Scholar
• Berman A, Plemmons RJ. Nonnegative matrix in the mathematical sciences. Philadelphia (PA): SIAM Publisher; 1994.
   Google Scholar
• Bai Z-Z. On the convergence of the multisplitting methods for the linear complementarity problem. SIAM J Matrix Anal Appl. 1999;21:67–78.
   Web of Science ®Google Scholar
• Frommer A, Mayer G. Convergence of relaxed parallel multisplitting methods. Linear Algebra Appl. 1989;119:141–152.
   Web of Science ®Google Scholar
• Hu J-G. Estimates of ||B-1C||∞ and their applications. Math Numer Sin. 1982;4:272–282.
   Google Scholar
• Dong J-L, Jiang M-Q. A modified modulus method for symmetric positive-definite linear complementarity problems. Numer Linear Algebra Appl. 2009;16:129–143.
   Web of Science ®Google Scholar