TY - JOUR
T1 - Norm Estimates for the Inverses of Strictly Diagonally Dominant $M$-Matrices and Linear Complementarity Problems
AU - Xiong , Yebo
AU - Liu , Jianzhou
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 487
EP - 514
PY - 2021
DA - 2021/05
SN - 11
DO - http://doi.org/10.4208/eajam.210820.161120
UR - https://global-sci.org/intro/article_detail/eajam/19138.html
KW - Strictly diagonally dominant matrix, $M$-matrix, linear complementarity problem, inverse, infinity norm bound.
AB - <p style="text-align: justify;">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.</p>