The Nekrasov condition is a form of diagonal dominance. Let \(A=[a_{ij}]\) be an \(n\times n\) complex matrix. Then \(A\) is a Nekrasov matrix if \(\left\vert a_{ii}\right\vert >h_{i}(A)\) for \(i=1,2,\dots,n\) where \[ h_{i}(A):=\sum_{j=1}^{i-1}\frac{|a_{ij}|}{|a_{jj}|}h_{j}(A)+\sum_{j=i+1}^{n}\left\vert a_{ij}\right\vert. \]
The authors give variations on different bounds on \(\left\Vert A^{-1}\right\Vert _{\infty}\) for a Nekrasov matrix. Numerical examples show that these bounds improve bounds given in [L. Yu. Kolotilina, J. Math. Sci., New York 199, No. 4, 432–437 (2014; Zbl 1309.15030); translation from Zap. Nauchn. Semin. POMI 419, 111–120 (2013); Y. Zhu and Y. Li, J. Yunnan Univ., Nat. Sci. 39, No. 1, 13–17 (2017; Zbl 1389.15011)].