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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {New classes of nonsingular matrices and upper bounds for their inverses},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     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/

[1] L. S. Dashnits, M. S. Zusmanovich, “O nekotorykh kriteriyakh regulyarnosti matrits i lokalizatsii ikh spektra”, Zh. vychisl. mat. mat. fiz., 10:5 (1970), 1092–1097 | MR | Zbl

[2] L. Yu. Kolotilina, “Otsenki opredelitelei i obratnykh dlya nekotorykh $H$-matrits”, Zap. nauchn. semin. POMI, 346, 2007, 81–102

[3] L. Yu. Kolotilina, “Otsenki beskonechnoi normy obratnykh k matritsam Nekrasova”, Zap. nauchn. semin. POMI, 419, 2013, 111–120

[4] L. Yu. Kolotilina, “Otsenki obratnykh dlya obobschennykh matrits Nekrasova”, Zap. nauchn. semin. POMI, 428, 2014, 182–195

[5] L. Yu. Kolotilina, “Nekotorye kharakterizatsii nekrasovskikh i $S$-nekrasovskikh matrits”, Zap. nauchn. semin. POMI, 428, 2014, 152–165

[6] L. Yu. Kolotilina, “Novye podklassy klassa $\mathcal{H}$-matrits i sootvetstvuyuschie otsenki obratykh matrits”, Zap. nauchn. semin. POMI, 453, 2016, 148–171

[7] L. Yu. Kolotilina, “O matritsakh Dashnitsa–Zusmanovicha (DZ) i matritsakh tipa Dashnitsa–Zusmanovicha (DZT) i ikh obratnykh”, Zap. nauchn. semin. POMI, 472, 2018, 145–165

[8] L. Yu. Kolotilina, “Matritsy nekrasovskogo tipa i otsenki dlya ikh obratnykh”, Zap. nauchn. semin. POMI, 482, 2019, 169–183

[9] J. H. Ahlberg, E. N. Nilson, “Convergence properties of the spline fit”, J. Soc. Ind. Appl. Math., 11 (1963), 95–104 | DOI | MR | Zbl

[10] L. Cvetković, P.-F. Dai, K. Doroslovac̆ki, Y.-T. Li, “Infinity norm bounds for the inverse of Nekrasov matrices”, Appl. Math. Comput., 219 (2013), 5020–5024 | MR | Zbl

[11] L. Cvetković, V. Kostić, K. Doroslovac̆ki, “Max-norm bounds for the inverse of $S$-Nekrasov matrices”, Appl. Math. Comput., 218 (2012), 9498–9503 | MR | Zbl

[12] L. Cvetković, V. Kostić, M. Nedović, “Generalizations of Nekrasov matrices and applications”, Open Math., 13 (2015), 96–105 | MR | Zbl

[13] L. Cvetković, V. Kostić, S. Raus̆ki, “A new subclass of $H$-matrices”, Appl. Math. Comput., 208 (2009), 206–210 | MR | Zbl

[14] Y. M. Gao, X. H. Wang, “Criteria for generalized diagonal dominant and $M$-matrices”, Linear Algebra Appl., 169 (2009), 257–268 | DOI | MR

[15] C. Li, L. Cvetković, Y. Wei, J. Zhao, “An infinity norm bound for the inverse of Dashnic–Zusmanovich type matrices with applications”, Linear Algebra Appl., 565 (2019), 99–122 | DOI | MR | Zbl

[16] N. Morac̆a, “Upper bounds for the infinity norm of the inverse of $SDD$ and ${\mathcal S}-SDD$ matrices”, J. Comput. Appl. Math., 206 (2007), 666–678 | DOI | MR | Zbl

[17] A. Ostrowski, “Über die Determinanten mit überwiegender Hauptdiagonale”, Comment. Math. Helv., 10 (1937), 69–96 | DOI | MR

[18] F. Robert, “Blocs-H-matrices et convergence des méthodes itérative”, Linear Algebra Appl., 2 (1969), 223–265 | DOI | MR | Zbl

[19] J. M. Varah, “A lower bound for the smallest singular value of a matrix”, Linear Algebra Appl., 11 (1975), 3–5 | DOI | MR | Zbl

[20] Y. Wang, L. Gao, “An improvement of the infinity norm bound for the inverse of $\{P_1,P_2\}$-Nekrasov matrices”, J. Ineq. Appl., 177 (2019) | MR