张丽丽
张丽丽. 关于线性互补问题的模系矩阵分裂迭代方法[J]. 计算数学, 2012, 34(4): 373-386.
Zhang Lili. ON MODULUS-BASED MATRIX SPLITTING ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS[J]. Mathematica Numerica Sinica, 2012, 34(4): 373-386.
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| [1] Bai Z Z. A class of two-stage iterative methods for systems of weakly nonlinear equations[J].Numer. Algorithms, 1997, 14: 295-319.[2] Bai Z Z. Parallel multisplitting two-stage iterative methods for large sparse systems of weaklynonlinear equations[J]. Numer. Algorithms, 1997, 15: 347-372.[3] Bai Z Z. On the convergence of the multisplitting methods for the linear complementarity problem[J]. SIAM J. Matrix Anal. Appl., 1999, 21: 67-78.[4] Bai Z Z. Convergence analysis of the two-stage multisplitting method[J]. Calcolo, 1999, 36: 63-74.[5] Bai Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Numer. Linear Algebra Appl., 2010, 17: 917-933.[6] Bai Z Z and Evans D J. Matrix multisplitting relaxation methods for linear complementarityproblems[J]. Int. J. Comput. Math., 1997, 63: 309-326.[7] Bai Z Z and Evans D J. Matrix multisplitting methods with applications to linear complementarityproblems: parallel synchronous and chaotic methods[J]. Réseaux et Systèmes Répartis:Calculateurs Parallelès, 2001, 13: 125-154.[8] Bai Z Z, Sun J C and Wang D R. A unified framework for the construction of various matrixmultisplitting iterative methods for large sparse system of linear equations[J]. Comput. Math.Appl., 1996, 32: 51-76.[9] Bai Z Z and Zhang L L. Modulus-based synchronous multisplitting iteration methods for linearcomplementarity problems[J]. Numer. Linear Algebra Appl., 2012, DOI: 10.1002/nla.1835.[10] Bai Z Z and Zhang L L. Modulus-based synchronous two-stage multisplitting iteration methodsfor linear complementarity problems[J]. Numer. Algorithms, 2012, DOI: 10.1007/s11075-012-9566-x.[11] Berman A and Plemmons R J. Nonnegative Matrices in the Mathematical Sciences, AcademicPress, New York, 1979.[12] Cottle R W, Pang J S and Stone R E. The Linear Complementarity Problem, Academic Press,San Diego, 1992.[13] Dong J L and Jiang M Q. A modified modulus method for symmetric positive-definite linearcomplementarity problems[J]. Numer. Linear Algebra Appl., 2009, 16: 129-143.[14] Ferris M C and Pang J S. Engineering and economic applications of complementarity problems[J].SIAM Rev., 1997, 39: 669-713.[15] Frommer A and Mayer G. Convergence of relaxed parallel multisplitting methods[J]. LinearAlgebra Appl., 1989, 119: 141-152.[16] Frommer A and Szyld D B. H-splittings and two-stage iterative methods[J]. Numer. Math., 1992,63: 345-356.[17] Hadjidimos A. Accelerated overrelaxation method[J]. Math. Comput., 1978, 32: 149-157.[18] Hadjidimos A and Tzoumas M. Nonstationary extrapolated modulus algorithms for the solutionof the linear complementarity problem[J]. Linear Algebra Appl., 2009, 431: 197-210.[19] Hadjidimos A and Yeyios A. Symmetric accelerated overrelaxation (SAOR) method[J]. Math.Comput. Simul., 1982, 24: 72-76.[20] Hu J G. Scaling transformation and convergence of splittings of matrix[J]. Math. Numer. Sinica,983, 5: 72-78.[21] Lemke C E and Howson J T. Equilibrium points of bimatrix games[J]. SIAM J. Appl. Math.,1964, 12: 413-423.[22] Machida N, Fukushima M and Ibaraki T. A multisplitting method for symmetric linear complementarityproblems[J]. J. Comput. Appl. Math., 1995, 62: 217-227.[23] Murty K G. Linear Complementarity, Linear and Nonlinear Programming, Heldermann-Verlag,Berlin, 1988.[24] O’Leary D P and White R E. Multi-splittings of matrices and parallel solution of linear systems[J]. SIAM J. Algebraic Discrete Methods, 1985, 6: 630-640.[25] Schäfer U. On the modulus algorithm for the linear complementarity problem[J]. Oper. Res.Lett., 2004, 32: 350-354.[26] Szyld D B and Jones M T. Two-stage and multisplitting methods for the parallel solution oflinear systems[J]. SIAM J. Matrix Anal. Appl., 1992, 13: 671-679.[27] Van Bokhoven W M G. Piecewise-linear Modelling and Analysis, Proefschrift, Eindhoven, 1981.[28] Varga R S. Matrix Iterative Analysis, 2nd Edition, Springer, Berlin, 2000.[29] Zhang L L. Two-step modulus-based matrix splitting iteration method for linear complementarityproblems[J]. Numer. Algorithms, 2011, 57: 83-99.[30] Zhang L L. Two-stage multisplitting iteration methods using modulus-based matrix splitting asinner iteration for linear complementarity problems, submitted.[31] Zhang L L. Two-step modulus-based synchronous multisplitting iteration methods for linearcomplementarity problems, submitted. |
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