Error bounds for linear complementarity problems of Nekrasov matrices

We present error bounds for the linear complementarity problem when the involved matrix is a Nekrasov matrix and also when it is a Σ$\Sigma $-Nekrasov matrix. The new bounds can improve considerably other previous bounds.

[1]  Vladimir Kostic,et al.  Max-norm bounds for the inverse of S-Nekrasov matrices , 2012, Appl. Math. Comput..

[2]  Vladimir Kostic,et al.  A new subclass of H-matrices , 2009, Appl. Math. Comput..

[3]  Olvi L. Mangasarian,et al.  New Error Bounds for the Linear Complementarity Problem , 1994, Math. Oper. Res..

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

[5]  Ksenija Doroslovački,et al.  Infinity norm bounds for the inverse of Nekrasov matrices , 2011, Appl. Math. Comput..

[6]  T. Szulc Some remarks on a theorem of Gudkov , 1995 .

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

[8]  Yang Jin An Iterative Criterion for H-matrices , 2006 .

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

[10]  Juan Manuel Peña,et al.  Error bounds for the linear complementarity problem with a Σ-SDD matrix , 2013 .

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

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

[13]  Juan Manuel Peña,et al.  Error bounds for linear complementarity problems involving BS-matrices , 2012, Appl. Math. Lett..

[14]  A. Hadjidimos,et al.  Is A∈Cn,n a general H-matrix? , 2012 .

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

[16]  Apostolos Hadjidimos,et al.  A New Iterative Criterion for H-Matrices , 2006, SIAM J. Matrix Anal. Appl..

[17]  Ping-Fan Dai,et al.  Error bounds for linear complementarity problems for SB-matrices , 2012, Numer. Algorithms.

[18]  Ping-Fan Dai,et al.  Error bounds for linear complementarity problems of QN-matrices , 2011, Calcolo.