Lei Gao

The weighted subdirect sum of matrices plays a fundamental role in applications involving overlapping structures, such as multilayer network analysis and overlapping block iterative methods for solving linear systems. In this paper, some sufficient conditions are presented to ensure that the weighted subdirect sum of Nekrasov matrices is in the class of Nekrasov matrices. We obtain, in particular, that the weighted $1$-subdirect sum of a Nekrasov matrix and a strictly diagonally dominant matrix remains a Nekrasov matrix. Theoretical results are complemented by numerical examples demonstrating the validity and applicability of the proposed conditions.

An error bound for BR?-matrices linear complementarity problems (LCPs) is given by Garc?a- Esnaola and Pe?a in the paper (Calcolo, 54(3), 813-822, 2017). However, this bound is not effective for BR?-matrices with a non-positive vector ?. In this paper, based on the Schur complement, some error bounds involving a parameter for LCPs of BR?-matrices with a non-positive vector ? are presented, and the optimal values of these error bounds are also determined. Numerical examples are performed to illustrate the effectiveness of the obtained bounds.

Institute of Mathematics of the Czech Academy of Sciences