• 论文 • 上一篇
张丽丽1, 任志茹2
张丽丽, 任志茹. 改进的分块模方法求解对角占优线性互补问题[J]. 计算数学, 2021, 43(3): 401-412.
Zhang Lili, Ren Zhiru. AN IMPROVED BLOCK MODULUS METHOD FOR DIAGONALLY DOMINANT LINEAR COMPLEMENTARITY PROBLEMS[J]. Mathematica Numerica Sinica, 2021, 43(3): 401-412.
Zhang Lili1, Ren Zhiru2
MR(2010)主题分类:
分享此文:
[1] Murty K G. Linear Complementarity, Linear and Nonlinear Programming[M]. Berlin:Heldermann-Verlag, 1988. [2] Cottle R W, Pang J S, Stone R E. The Linear Complementarity Problem[M]. San Diego:Academic Press, 1992. [3] Ferris M C, Pang J S. Engineering and economic applications of complementarity problems[J]. SIAM Rev., 1997, 39(4):669-713. [4] van Bokhoven W M G. Piecewise-Linear Modelling and Analysis[M]. Eindhoven:Proefschrift, 1981. [5] Kappel N W, Watson L T. Iterative algorithms for the linear complementarity problem[J]. Int. J. Comput. Math., 1986, 19(3-4):273-297. [6] Dong J L, Jiang M Q. A modified modulus method for symmetric positive-definite linear complementarity problems[J]. Numer. Linear Algebra Appl., 2009, 16(2):129-143. [7] Hadjidimos A, Tzoumas M. Nonstationary extrapolated modulus algorithms for the solution of the linear complementarity problem[J]. Linear Algebra Appl., 2009, 431(1-2):197-210. [8] Bai Z Z. Modulus-based matrix splitting iteration methods for linear complementarity problems[J]. Numer. Linear Algebra Appl., 2010, 17(6):917-933. [9] Zhang L L. Two-step modulus-based matrix splitting iteration method for linear complementarity problems[J]. Numer. Algorithms, 2011, 57(1):83-99. [10] 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. [11] Bai Z Z, Zhang L L. Modulus-based synchronous multisplitting iteration methods for linear complementarity problems[J]. Numer. Linear Algebra Appl., 2013, 20(3):425-439. [12] Li W. A general modulus-based matrix splitting method for linear complementarity problems of H-matrices[J]. Appl. Math. Lett., 2013, 26(12):1159-1164. [13] Zheng N, Yin J F. Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem[J]. Numer. Algorithms, 2013, 64(2):245-262. [14] Zheng N, Yin J F. Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an H+-matrix[J]. J. Comput. Appl. Math., 2014, 260:281-293. [15] Xu W W, Liu H. A modified general modulus-based matrix splitting method for linear complementarity problems of H-matrices[J]. Linear Algebra Appl., 2014, 458:626-637. [16] Dong J L, Gao J B, Ju F J, Shen J H. Modulus methods for nonnegatively constrained image restoration[J]. SIAM J. Imaging Sciences, 2016, 9(3):1226-1246. [17] Li W, Zheng H. A preconditioned modulus-based iteration method for solving linear complementarity problems of H-matrices[J]. Linear Multilinear Algebra, 2016, 64(7):1390-1403. [18] Wu S L, Li C X. Two-sweep modulus-based matrix splitting iteration methods for linear complementarity problems[J]. J. Comput. Appl. Math., 2016, 302:327-339. [19] Bai Z Z, Zhang L L. Modulus-based multigrid methods for linear complementarity problems[J]. Numer. Linear Algebra Appl., 2017, 24(6):e2105. [20] Yang X, Huang Y M, Sun L. A modulus iteration method for retinex problem[J]. Numer. Linear Algebra Appl., 2018, 25(6):e2207. [21] Zhang L T, Jiang D D, Zuo X Y, Zhao Y C, Zhang Y F. Relaxed modulus-based synchronous multisplitting multi-parameter methods for linear complementarity problems[J]. Mobile Netw. Appl., 202126(2):745-754. [22] Hadjidimos A, Zhang L L. Comparison of three classes of algorithms for the solution of the linear complementarity problem with an H+-matrix[J]. J. Comput. Appl. Math., 2018, 336:175-191. [23] Berman A, Plemmons R J. Nonnegative Matrices in the Mathematical Sciences[M]. New York:Academic Press, 1979. [24] Bai Z Z. On the convergence of the multisplitting methods for the linear complementarity problem[J]. SIAM J. Matrix Anal. Appl., 1999, 21(1):67-78. [25] Frommer A, Szyld D B. H-splittings and two-stage iterative methods[J]. Numer. Math., 1992, 63(1):345-356. [26] Varga R S. Matrix Iterative Analysis[M]. Berlin and Heidelberg:Springer-Verlag, 2000. [27] Frommer A, Mayer G. Convergence of relaxed parallel multisplitting methods[J]. Linear Algebra Appl., 1989, 119:141-152. [28] 胡家赣.||B-1A||的估计及其应用[J]. 计算数学, 1982, 4(3):272-282. [29] 胡家赣.尺度变换和矩阵分解的收敛性[J]. 计算数学, 1983, 5(1):72-78. [30] Hadjidimos A, Lapidakis M, Tzoumas M. On iterative solution for linear complementarity problem with an H+-matrix[J]. SIAM J. Matrix Anal. Appl., 2012, 33(1):97-110. [31] Wang A, Cao Y, Chen J X. Modified Newton-type iteration methods for generalized absolute value equations[J]. J. Optim. Theory Appl., 2019, 181(1):216-230. [32] Alanelli M, Hadjidimos A. A new iterative criterion for H-matrices[J]. SIAM J. Matrix Anal. Appl., 2006, 29(1):160-176. [33] Carlson D, Markham T L. Schur complements of diagonally dominant matrices[J]. Czech. Math. J., 1979, 29(2):246-251. |
[1] | 余妍妍, 代新杰, 肖爱国. 非自治刚性随机微分方程正则EM分裂方法的收敛性和稳定性[J]. 计算数学, 2022, 44(1): 19-33. |
[2] | 邵新慧, 亢重博. 基于分数阶扩散方程的离散线性代数方程组迭代方法研究[J]. 计算数学, 2022, 44(1): 107-118. |
[3] | 古振东. 非线性弱奇性Volterra积分方程的谱配置法[J]. 计算数学, 2021, 43(4): 426-443. |
[4] | 包学忠, 胡琳. 随机变延迟微分方程平衡方法的均方收敛性与稳定性[J]. 计算数学, 2021, 43(3): 301-321. |
[5] | 胡雅伶, 彭拯, 章旭, 曾玉华. 一种求解非线性互补问题的多步自适应Levenberg-Marquardt算法[J]. 计算数学, 2021, 43(3): 322-336. |
[6] | 李旭, 李明翔. 连续Sylvester方程的广义正定和反Hermitian分裂迭代法及其超松弛加速[J]. 计算数学, 2021, 43(3): 354-366. |
[7] | 邱泽山, 曹学年. 带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式[J]. 计算数学, 2021, 43(2): 210-226. |
[8] | 袁光伟. 非正交网格上满足极值原理的扩散格式[J]. 计算数学, 2021, 43(1): 1-16. |
[9] | 朱梦姣, 王文强. 非线性随机分数阶微分方程Euler方法的弱收敛性[J]. 计算数学, 2021, 43(1): 87-109. |
[10] | 李天怡, 陈芳. 求解一类分块二阶线性方程组的QHSS迭代方法[J]. 计算数学, 2021, 43(1): 110-117. |
[11] | 丁戬, 殷俊锋. 求解一类非线性互补问题的松弛two-sweep模系矩阵分裂迭代法[J]. 计算数学, 2021, 43(1): 118-132. |
[12] | 尹江华, 简金宝, 江羡珍. 凸约束非光滑方程组一个新的谱梯度投影算法[J]. 计算数学, 2020, 42(4): 457-471. |
[13] | 古振东, 孙丽英. 非线性第二类Volterra积分方程的Chebyshev谱配置法[J]. 计算数学, 2020, 42(4): 445-456. |
[14] | 吴敏华, 李郴良. 求解带Toeplitz矩阵的线性互补问题的一类预处理模系矩阵分裂迭代法[J]. 计算数学, 2020, 42(2): 223-236. |
[15] | 张纯, 贾泽慧, 蔡邢菊. 广义鞍点问题的改进的类SOR算法[J]. 计算数学, 2020, 42(1): 39-50. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||