双严格对角占优矩阵线性互补问题的最优误差界
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摘要
针对H-矩阵线性互补问题误差界的估计式,利用双严格对角占优矩阵的性质和函数的单调性,得到了含有参数的双严格对角占优矩阵线性互补问题的误差界,并确定了其最优值.
For the error bounds for linear complementary problems of H-matrix, using the properties of double strictly diagonally dominant matrices and the monotonicity of function, the optimal value of error bound with a parameter of linear complementary problem of double strictly diagonally dominant matrices is obtained, and then its optimal value is determined.
For the error bounds for linear complementary problems of H-matrix, using the properties of double strictly diagonally dominant matrices and the monotonicity of function, the optimal value of error bound with a parameter of linear complementary problem of double strictly diagonally dominant matrices is obtained, and then its optimal value is determined.
引文
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[13]李艳艳,蒋建新,李耀堂.严格对角占优M-矩阵A的‖A-1‖∞上界估计式的改进[J].云南大学学报:自然科学版,2015,37(1):5-8.Li Y Y,Jiang J X,Li Y T.The improved upper bound estimation of‖A-1‖∞for strictly diagonally dominant M-matrices[J].Journal of Yunnan University:Natural Sciences Edition,2015,37(1):5-8.
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[2]Ferris M S,Pang J S.Engineering and economic applications of complementarity problems[J].SIAM Rev,1997,39(4):669-713.DOI:10.1137/S0036144595285963.
[3]Pe?a J M.A class of P-matrices with applications to the localization of the eigenvalues of areal matrix[J].SIAM J Matrix Anal Appl,2001,22(4):1027-1037.DOI:10.1137/S0895479800370342.
[4]Chen X,Xiang S.Perturbation bounds of P-matrix linear complementarity problems[J].SIAM J Optim,2007,18:1250-1265.
[5]Chen X,Xiang S.Computation of error bounds for P-matrix linear complementarity problems[J].Math Program,2006,106(3):513-525.DOI:10.1007/s10107-005-0645-9.
[6]Bai Z Z.On the convergence of the multisplitting methods for the linear complementarity problem[J].SIAM Journal on Matrix Analysis And Applications,1999,21(1):67-78.DOI:10.1137/S0895479897324032.
[7]García-Esnaola M,Pe?a J M.Error bounds for linear complementarity problems of Nekrasov matrices[J].Numer.Algor,2014,67(3):655-667.DOI:10.1007/s11075-013-9815-7.
[8]García-Esnaola M,Pe?a J M.B-Nekrasov matrices and error bounds for linear complementarity problems[J].Numer Algor,2016,72(2):435-445.DOI:10.1007/s11075-015-0054-y.
[9]Dai P F,Li J C,Li Y T,et al.Error bounds for inear complementarity problems of QN-matrices[J].Calcolo,2016,53(4):647-657.DOI:10.1007/s10092-015-0167-7.
[10]García-Esnaola M,Pe?a J M.A comparison of error bounds for linear complementarity problems of H-matrices[J].Linear Algebra Appl,2010,433(5):956-964.DOI:10.1016/j.laa.2010.04.024.
[11]Li B S,Tsatsomeros M J.TSATSOMEROS.Doubly diagonally dominant matrices[J].Linear Algebra Appl,1997,26(1-3):221-235.
[12]Berman A,Plemmons R.Nonnegative matrices in the mathematical sciences[M].Philadelphia:SIAM,1994.
[13]李艳艳,蒋建新,李耀堂.严格对角占优M-矩阵A的‖A-1‖∞上界估计式的改进[J].云南大学学报:自然科学版,2015,37(1):5-8.Li Y Y,Jiang J X,Li Y T.The improved upper bound estimation of‖A-1‖∞for strictly diagonally dominant M-matrices[J].Journal of Yunnan University:Natural Sciences Edition,2015,37(1):5-8.
[14]Varga R S.On diagonal dominance argumenets for bounding‖A-1‖∞[J].Linear Algebra Appl,1976,14(3):211-217.DOI:10.1016/0024-3795(76)90067-7.