Geodesic
New classes of nonsingular matrices and upper bounds for their inverses
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 184-200

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The paper introduces new classes of nonsingular matrices, which extend some known subclasses of the class of nonsingular $\mathcal{H}$-matrices, such as the Nekrasov, $Q$-Nekrasov, $\{P_1,P_2\}$-Nekrasov, and DZ matrices. For matrices in the classes introduced, upper bounds for $\|A^{-1}\|_\infty$ are derived (in a unified manner) and shown to improve the known bounds for matrices from the corresponding subclasses of nonsingular $\mathcal{H}$-matrices. 
@article{ZNSL_2019_482_a12,
     author = {L. Yu. Kolotilina},
     title = {New classes of nonsingular matrices and upper bounds for their inverses},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {184--200},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a12/}
}
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L. Yu. Kolotilina. New classes of nonsingular matrices and upper bounds for their inverses. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 184-200. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a12/