Geodesic
Some bounds for inverses involving matrix sparsity pattern
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 201-219

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The paper considers some subclasses of the class of nonsingular $\mathcal{H}$-matrices whose definitions involve matrix sparsity pattern. For matrices $A$ in these subclasses, upper bounds for $\|A^{-1}\|_\infty$ are derived and shown to be sharper than the corresponding bounds ignoring matrix sparsity. 
@article{ZNSL_2019_482_a13,
     author = {L. Yu. Kolotilina},
     title = {Some bounds for inverses involving matrix sparsity pattern},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {201--219},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a13/}
}
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L. Yu. Kolotilina. Some bounds for inverses involving matrix sparsity pattern. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 201-219. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a13/