An infinity norm bound for the inverse of Dashnic–Zusmanovich type matrices with applications

Abstract

© 2018 Elsevier Inc. An upper bound for the infinity norm for the inverse of Dashnic–Zusmanovich type matrices is given. It is proved that the upper bound is sharper than the well-known Varah's bound for strictly diagonally dominant matrices. By introducing a new subclass of P-matrices: Dashnic–Zusmanovich type B-matrices (DZ-type-B-matrices), and using the proposed infinity norm bound, an error bound is given for the linear complementarity problems of DZ-type-B-matrices. We also give a new pseudospectra localization to measure the distance to instability.