Error bounds for linear complementarity problems of QN-matrices

Doubly B-matrices (DB-matrices), which properly contain B-matrices, are introduced by Pena (2003) [2]. In this paper we present error bounds for the linear complementarity problem when the matrix involved is a DB-matrix and a new bound for linear complementarity problem of a B-matrix. The numerical examples show that the bounds are sharp.

[1]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[2]  Juan Manuel Peña,et al.  Error bounds for linear complementarity problems for B-matrices , 2009, Appl. Math. Lett..

[3]  J. Pang,et al.  Error bounds for the linear complementarity problem with a P-matrix , 1990 .

[4]  Juan Manuel Peña,et al.  On an alternative to Gerschgorin circles and ovals of Cassini , 2003, Numerische Mathematik.

[5]  Uwe Schäfer,et al.  A Linear Complementarity Problem with a P-Matrix , 2004, SIAM Rev..

[6]  Juan Manuel Peña,et al.  A comparison of error bounds for linear complementarity problems of H-matrices , 2010 .

[7]  J. Mason,et al.  Near-best L, Approximations by Fourier, Taylor and Laurent Series , 1984 .

[8]  Ya-Xiang Yuan,et al.  Componentwise error bounds for linear complementarity problems , 2011 .

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

[10]  Xiaojun Chen,et al.  Perturbation Bounds of P-Matrix Linear Complementarity Problems , 2007, SIAM J. Optim..

[11]  Juan M. Peña,et al.  A Class of P-Matrices with Applications to the Localization of the Eigenvalues of a Real Matrix , 2000, SIAM J. Matrix Anal. Appl..

[12]  Michael J. Tsatsomeros,et al.  Doubly diagonally dominant matrices , 1997 .

[13]  Xiaojun Chen,et al.  Computation of Error Bounds for P-matrix Linear Complementarity Problems , 2006, Math. Program..

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