Geodesic
$\mathrm{SDD}_1$ matrices and their generalizations
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 74-93

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The paper considers the classes of $\mathrm{GSDD}_1$, $\mathrm{GSDD}_1^*$, and $SD$-$\mathrm{SDD}$ matrices, which contain the class of $\mathrm{SDD}$ (strictly diagonally dominant) matrices and are contained in the class of nonsingular $\mathcal{H}$-matrices. New upper bounds on $\|A^{-1}\|_\infty$ for $\mathrm{GSDD}_1$, $\mathrm{GSDD}_1^*$, and $SD$-$\mathrm{SDD}$ matrices $A$, generalizing known upper bounds for $S$-$\mathrm{SDD}$, $\mathrm{SDD}_1^*$, and $\mathrm{GSDD}_1$ matrices, are established and compared. 
@article{ZNSL_2023_524_a6,
     author = {L. Yu. Kolotilina},
     title = {$\mathrm{SDD}_1$ matrices and their generalizations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {74--93},
     publisher = {mathdoc},
     volume = {524},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a6/}
}
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L. Yu. Kolotilina. $\mathrm{SDD}_1$ matrices and their generalizations. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXVI, Tome 524 (2023), pp. 74-93. http://geodesic.mathdoc.fr/item/ZNSL_2023_524_a6/