Geodesic
Nekrasov type matrices and upper bounds for their inverses
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 169-183 
L. Yu. Kolotilina. Nekrasov type matrices and upper bounds for their inverses. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 169-183. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a11/
@article{ZNSL_2019_482_a11,
     author = {L. Yu. Kolotilina},
     title = {Nekrasov type matrices and upper bounds for their inverses},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {169--183},
     year = {2019},
     volume = {482},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a11/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper considers the so-called $P$-Nekrasov and $\{P_1, P_2\}$-Nekrasov matrices, defined in terms of permutation matrices $P, P_1, P_2$, which generalize the well-known notion of Nekrasov matrices. For such matrices $A$, available upper bounds on $\|A^{-1}\|_\infty$ are recalled, and new upper bounds for the $P$-Nekrasov and $\{P_1, P_2\}$-Nekrasov matrices are suggested. It is shown that the latter bound generally improves the earlier bounds, as well as the bound for the inverse of a $P$-Nekrasov matrix and the classical bound for the inverse of a strictly diagonally dominant matrix.

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

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

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

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

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

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

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

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

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

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

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

[12] 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