On bounding inverses to Nekrasov matrices in the infinity norm

A new upper bound on the infinity norm of the inverse to a Nekrasov matrix, improving two recent bounds by L. Cvetković et al. [L. Cvetković, P.-F. Dai, K. Doroslovac̆ki, and Y.-T. Li, Infinity norm bounds for the inverse of Nekrasov matrices, Appl. Math. Comput., 219, 5020–5024 (2013)], is obtained. Also it is shown that for a strictly diagonally dominant matrix, the bound suggested improves the classical Varah upper bound.