Error bounds for linear complementarity problems of weakly chained diagonally dominant B-matrices

Abstract

In this paper, new error bounds for the linear complementarity problem are obtained when the involved matrix is a weakly chained diagonally dominant B-matrix. The proposed error bounds are better than some existing results. The advantages of the results obtained are illustrated by numerical examples.

An improvement of the infinity norm bound for the inverse of $\{P_{1},P_{2}\}$-Nekrasov matrices

“…It is well known that H-matrices are widely used in many subjects such as numerical algebra, the control system, mathematical physics, economics, and dynamical system theory [1,2,4,20]. An important problem among them is to find upper bounds for the infinity norm of the inverse of H-matrices, because it can be used to the convergence analysis of matrix splitting and matrix multi-splitting iterative methods for solving large sparse systems of linear equations [18], as well as linear complementarity problems [10][11][12][13]19]. For example, when solving linear systems in practice, it is important to have an economical method for estimating the condition number κ(A) of the matrix of coefficients, which shows how 'ill' the systems could be.…”

New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

“…for more details, see [1][2][3]. Here, the linear complementarity problem (LCP) is to nd a vector x ∈ R n such that inverse matrix from (2), several easily computable bounds for LCPs were derived for the di erent subclass of P-matrices, such as positively diagonal Nekrasov matrices [6,7], S-Nekrasov matrices [8,9], QN-matrices [10,11], S-QN-matrices [12], B-matrices [13][14][15], DB-matrices [16], SB-matrices [17,18], MB-matrices [2], B-Nekrasov matrices [7,19,20], B R π -matrices [21,22], Dashnic-Zusmanovich type matrices [23], and weakly chained diagonally dominant B-matrices [24][25][26]. In [27], García-Esnaola and Peña present an error bound for the LCP(M, q) involved with Σ-SDD matrices, this bound involves a parameter and works only for Σ-SDD matrices but not strictly diagonally dominant matrices.…”

An alternative error bound for linear complementarity problems involving B S $B^{S}$ -matrices

“…An interesting problem for the is to estimate since it can often be used to bound the error [ 5 ], that is, where , with for each , , and in which the min operator denotes the componentwise minimum of two vectors; for more details, see [ 1 , 6 – 14 ] and the references therein.…”