Geodesic
A block generalization of Nekrasov matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 138-155

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The paper introduces the so-called generalized Nekrasov (GN) matrices, which provide a block extension of the conventional Nekrasov matrices. Basic properties of GN matrices are studied. In particular, it is proved that the GN matrices form a subclass of nonsingular $\mathcal{H}$-matrices and this subclass is closed with respect to Schur complements obtained by eliminating leading principal block submatrices. Also an upper bound for the $l_\infty$-norm of the inverse to a GN matrix is obtained, which generalizes the known bound for Nekrasov matrices. The case of block two-by-two GN matrices with scalar first diagonal block, which prove to be Dashnic–Zusmanovich matrices of the first type, is considered separately. The bounds obtained are applied to SDD matrices. 
@article{ZNSL_2020_496_a10,
     author = {L. Yu. Kolotilina},
     title = {A block generalization of {Nekrasov} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {138--155},
     publisher = {mathdoc},
     volume = {496},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a10/}
}
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L. Yu. Kolotilina. A block generalization of Nekrasov matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 138-155. http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a10/