Norm Estimates for the Inverses of Strictly Diagonally Dominant $M$-Matrices and Linear Complementarity Problems

Abstract

A partition reduction method is used to obtain two new upper bounds for the inverses of strictly diagonally dominant $M$-matrices. The estimates are expressed via the determinants of third order matrices. Numerical experiments with various random matrices show that they are stable and better than the estimates presented in literature. We use these upper bounds in order to improve known error estimates for linear complementarity problems with $B$-matrices.