Upper norm bounds for the inverse of locally doubly strictly diagonally dominant matrices with its applications in linear complementarity problems

In this paper, we present two error bounds for the linear complementarity problems (LCPs) of locally doubly strictly diagonally dominant (LDSDD) matrices. The error bounds are based on two upper norm bounds for the inverse of LDSDD matrices by using a new reduction method. The core of the reduction method lies in the particularity of the LDSDD matrices, which allows us to turn the problem into computing the counterpart of k-order doubly strictly diagonally dominant (DSDD) matrices through partition and summation. Many numerical experiments with lots of random matrices are presented to show the efficiency and superiority of our results.