Geodesic
Pseudoblock conditions of diagonal dominance
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 94-131

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The paper presents new pseudoblock diagonal-dominance conditions for matrices with fixed block partitioning, which generalize the pointwise $k$th-order diagonal-dominance conditions and pointwise circuit diagonal-dominance conditions. For matrices satisfying pseudoblock conditions, the singularity/nonsingularity problem is considered. In particular, for block $2\times 2$ matrices, certain known results are improved and generalized. Some eigenvalue inclusion regions corresponding to pseudoblock nonsingularity conditions are presented. 
@article{ZNSL_2005_323_a8,
     author = {L. Yu. Kolotilina},
     title = {Pseudoblock conditions of diagonal dominance},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {94--131},
     publisher = {mathdoc},
     volume = {323},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a8/}
}
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L. Yu. Kolotilina. Pseudoblock conditions of diagonal dominance. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 94-131. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a8/