Convergence of accelerated modulus-based matrix splitting iteration methods for linear complementarity problem with an H+-matrix

The theoretical analysis of the accelerated modulus-based matrix splitting iteration methods for the solution of the large sparse linear complementarity problem is further studied. The convergence conditions are presented by fully utilizing the H + -matrix property of the system matrix, and the optimal iteration parameters in accelerated modulus-based accelerated overrelaxation method are determined by minimizing the spectral radius of the iteration matrix. Numerical experiments further confirm the theoretical discussion, and show that the proposed methods accelerate the convergence of the modulus-based matrix splitting methods with less iteration steps and CPU time.

[1]  Zhong-Zhi Bai,et al.  The convergence of parallel iteration algorithms for linear complementarity problems , 1996 .

[2]  David J. Evans,et al.  Matrix Multisplitting Methods with Applications to Linear Complementarity Problems∶ Parallel Asynchronous Methods , 2002, Int. J. Comput. Math..

[3]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[4]  David J. Evans,et al.  Matrix multisplitting relaxation methods for linear complementarity problems , 1997, Int. J. Comput. Math..

[5]  O. Mangasarian.  Solution of symmetric linear complementarity problems by iterative methods , 1977 .

[6]  Daniel B. Szyld,et al.  Comparison theorems for weak splittings of bounded operators , 1990 .

[7]  Zhong-Zhi Bai,et al.  Modulus‐based matrix splitting iteration methods for linear complementarity problems , 2010, Numer. Linear Algebra Appl..

[8]  C. Cryer.  The Solution of a Quadratic Programming Problem Using Systematic Overrelaxation , 1971 .

[9]  D. Szyld,et al.  H-Splittings and two-stage iterative methods , 1992 .

[10]  Apostolos Hadjidimos,et al.  On Iterative Solution for Linear Complementarity Problem with an H+-Matrix , 2012, SIAM J. Matrix Anal. Appl..

[11]  Uwe Sch.  A Linear Complementarity Problem with a P-Matrix ∗ , 2004 .

[12]  Layne T. Watson,et al.  Iterative algorithms for the linear complementarity problem , 1986 .

[13]  Li-Li Zhang,et al.  Two-step modulus-based matrix splitting iteration method for linear complementarity problems , 2011, Numerical Algorithms.

[14]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[15]  Apostolos Hadjidimos,et al.  Nonstationary Extrapolated Modulus Algorithms for the solution of the Linear Complementarity Problem , 2009 .

[16]  Zhong-zhi,et al.  EXPERIMENTAL STUDY OF THE ASYNCHRONOUS MULTISPLITTING RELAXATION METHODS FOR THE LINEAR COMPLEMENTARITY PROBLEMS , 2002 .

[17]  Ning Zheng,et al.  Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem , 2012, Numerical Algorithms.

[18]  Mei-Qun Jiang,et al.  A modified modulus method for symmetric positive‐definite linear complementarity problems , 2009, Numer. Linear Algebra Appl..

[19]  Zhong-Zhi Bai,et al.  On the Convergence of the Multisplitting Methods for the Linear Complementarity Problem , 1999, SIAM J. Matrix Anal. Appl..

[20]  Katta G. Murty,et al.  Linear complementarity, linear and nonlinear programming , 1988 .

[21]  G. Dantzig,et al.  COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[22]  B. Ahn.  Solution of nonsymmetric linear complementarity problems by iterative methods , 1981 .

[23]  A. Frommer,et al.  Convergence of relaxed parallel multisplitting methods , 1989 .

[24]  Zhong-zhiBai,et al.  A CLASS OF ASYNCHRONOUS PARALLEL MULTISPLITTING RELAXATION METHODS FOR LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEMS , 2003 .

[25]  Ning Zheng,et al.  On the convergence of projected triangular decomposition methods for pricing American options with stochastic volatility , 2013, Appl. Math. Comput..

[26]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.