双边障碍问题的模系矩阵分裂迭代方法
|
摘要
针对一类双边障碍问题,提出了一类模系矩阵分裂迭代方法。该方法采用模系矩阵分裂迭代算法逐次子线性互补问题,最终求解的线性互补问题的解,即为双边障碍问题的解。通过分析方法的收敛性,数值结果表明了方法的有效性。
A modulus-based matrix splitting method is presented for solving a two-side obstacle problem,which solves some sub-linear complementarity problems by using the matrix splitting method.The solution of the final sub-linear complementarity problems is the solution of the two-side obstacle problem.The convergence is given,and the numerical results show that the proposed method is effective.
A modulus-based matrix splitting method is presented for solving a two-side obstacle problem,which solves some sub-linear complementarity problems by using the matrix splitting method.The solution of the final sub-linear complementarity problems is the solution of the two-side obstacle problem.The convergence is given,and the numerical results show that the proposed method is effective.
引文
[1]HARKER P T,PANG J S.Finite-dimensional variational inequality and nonlinear complementarity problems[J].Mathematical Programming,1990,48(2):161-220.
[2]MEYER G H.Free boundary problems with nonlinear source terms[J].Numerische Mathematic,1984,43:463-482.
[3]李董辉,曾金平.双边障碍问题的迭代法[J].数值计算与计算机应用,1994,(3):194-199.
[4]董晓亮,李郴良,何郁波,等.一类双边障碍问题的松弛型二级分裂并行算法[J].数学杂志,2011,31(2):323-330.
[5]李向阳,李金周.EAOR方法求解一类双边障碍问题[J].工程数学学报.2009,26(1):67-74.
[6]ZHOU S Z,ZENG J P.Monotonic iterative algorithms for an implicit two-side obstacle problems[J].Computers and Mathematics with Application,2002,41(3):31-40.
[7]BADEA L.On the Schwarz alternating method with more than two sub-domain for nonlinear monotone problems[J].SIAM Jour On Numerical Analysis,1991,28:179-204.
[8]STEPHEN C B.A comparison of algorithms for large scale mixed complementarity problems[J].Computational Optimization and Application,1997,7(1):3-25.
[9]BOKHOVEN V.Piecewise-linear Modelling and Analysis[M].ProefschiftEindhoven:TechnischeHogeschool Eindhoven,1981:67-79.
[10]DONG J L,JIANG M Q.A modified modulus method for symmetric positive linear complementarity problem[J].Numerical Linear Algebra Application,2009,16(2):129-143.
[11]BAI Z Z.Modulus-based matrix splitting iteration methods for linear complementarity problems[J].Numerical Linear Algebra Application,2010,17(6):917-933.
[12]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.
[13]XU W W.Modified modulus-based matrix splitting iteration methods for linear complementarity problems[J].Numerical Linear Applications,2015,22(4):748-760.
[14]HONG J T,LI C L.Modulus-based matrix splitting iteration methods for a class implicit complementarity[J].Numerical Linear Applications,2016,23(4):629-641.
[15]XIA Z C,LI C L.Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems[J].Applied Mathematics and Computation,2015,271:34-42.
[16]曾金平,周叔子.双障碍问题的等价线性互补问题[J].科学通报,1994,33(5):394-397.
[17]张磊,胡锡炎.关于线性互补问题的直接法[J].计算数学,1994,22(4):59-64.
[2]MEYER G H.Free boundary problems with nonlinear source terms[J].Numerische Mathematic,1984,43:463-482.
[3]李董辉,曾金平.双边障碍问题的迭代法[J].数值计算与计算机应用,1994,(3):194-199.
[4]董晓亮,李郴良,何郁波,等.一类双边障碍问题的松弛型二级分裂并行算法[J].数学杂志,2011,31(2):323-330.
[5]李向阳,李金周.EAOR方法求解一类双边障碍问题[J].工程数学学报.2009,26(1):67-74.
[6]ZHOU S Z,ZENG J P.Monotonic iterative algorithms for an implicit two-side obstacle problems[J].Computers and Mathematics with Application,2002,41(3):31-40.
[7]BADEA L.On the Schwarz alternating method with more than two sub-domain for nonlinear monotone problems[J].SIAM Jour On Numerical Analysis,1991,28:179-204.
[8]STEPHEN C B.A comparison of algorithms for large scale mixed complementarity problems[J].Computational Optimization and Application,1997,7(1):3-25.
[9]BOKHOVEN V.Piecewise-linear Modelling and Analysis[M].ProefschiftEindhoven:TechnischeHogeschool Eindhoven,1981:67-79.
[10]DONG J L,JIANG M Q.A modified modulus method for symmetric positive linear complementarity problem[J].Numerical Linear Algebra Application,2009,16(2):129-143.
[11]BAI Z Z.Modulus-based matrix splitting iteration methods for linear complementarity problems[J].Numerical Linear Algebra Application,2010,17(6):917-933.
[12]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.
[13]XU W W.Modified modulus-based matrix splitting iteration methods for linear complementarity problems[J].Numerical Linear Applications,2015,22(4):748-760.
[14]HONG J T,LI C L.Modulus-based matrix splitting iteration methods for a class implicit complementarity[J].Numerical Linear Applications,2016,23(4):629-641.
[15]XIA Z C,LI C L.Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems[J].Applied Mathematics and Computation,2015,271:34-42.
[16]曾金平,周叔子.双障碍问题的等价线性互补问题[J].科学通报,1994,33(5):394-397.
[17]张磊,胡锡炎.关于线性互补问题的直接法[J].计算数学,1994,22(4):59-64.