An improvement of the infinity norm bound for the inverse of { P 1 , P 2 } ${P_{1},P_{2}}$ -Nekrasov matrices

A new upper bound for the infinity norm for the inverse of $\{P_{1},P _{2}\}$ -Nekrasov matrices is given. It is proved that the upper bound is sharper than those in Cvetković et al. (Open Math. 13:96–105, 2015) and than well-known Varah’s bound for strictly diagonally dominant matrices. Numerical examples are given to illustrate the corresponding results.