The paper considers upper bounds for the infinity norm of the inverse for matrices in two subclasses of the class of (nonsingular) H-matrices, both of which contain the class of Nekrasov matrices. The first one has been introduced recently and consists of the so-called S-Nekrasov matrices. For S-Nekrasov matrices, the known bounds are improved. The second subclass consists of the socalled QN- (quasi-Nekrasov) matrices, which are defined in the present paper. For QN-matrices, an upper bound on the infinity norm of the inverses is established. It is shown that in application to Nekrasov matrices the new bounds are generally better than the known ones. Bibliography: 15 titles.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Cvetković, P.-F. Dai, K. Doroslovački, and Y.-T. Li, “Infinity norm bounds for the inverse of Nekrasov matrices,” Appl. Math. Comput., 219, 5020–5024 (2013).
L. Cvetković, V. Kostić, and K. Doroslovački, “Max-norm bounds for the inverse of SNekrasov matrices,” Appl. Math. Comput., 218, 9498–9503 (2012).
L. Cvetković, V. Kostić, and S. Rauški, “A new subclass of H-matrices,” Appl. Math. Comput., 208, 206–210 (2009).
L. Cvetković, V. Kostić, and R. Varga, “A new Geršgorin-type eigenvalue inclusion area,” ETNA, 18, 73–80 (2004).
Y. M. Gao and X. H. Wang, “Criteria for generalized diagonal dominant and M-matrices,” Linear Algebra Appl., 169, 257–268 (2009).
V. V. Gudkov, “On a criterion of matrices non-singularity,” in: Latv. Math. Yearbook [in Russian], Riga (1966), pp. 385–390.
L. Yu. Kolotilina, “Pseudoblock conditions of diagonal dominance,” Zap. Nauchn. Semin. POMI, 323, 94–131 (2005).
L. Yu. Kolotilina, “Bounds for the determinants and inverses of certain H-matrices,” Zap. Nauchn. Semin. POMI, 346, 81–102 (2007).
L. Yu. Kolotilina, “On bounding inverses to Nekrasov matrices in the infinity norm,” Zap. Nauchn. Semin. POMI, 419, 111–120 (2013).
L. Yu. Kolotilina, “Some characterizations of Nekrasov and S-Nekrasov matrices,” Zap. Nauchn. Semin. POMI, 428, 152–165 (2014).
N. Morača, “Upper bounds for the infinity norm of the inverse of SDD and S – SDD matrices,” J. Comput. Appl. Math., 206, 666–678 (2007).
A. Ostrowski, “¨Uber die Determinanten mit ¨uberwiegender Hauptdiagonale,” Comment. Math. Helv., 10, 69–96 (1937).
F. Robert, “Blocs-H-matrices et convergence des méthodes itérative,” Linear Algebra Appl., 2, 223–265 (1969).
J. M. Varah, “A lower bound for the smallest singular value of a matrix,” Linear Algebra Appl., 11, 3–5 (1975).
R. S. Varga, Geršgorin and His Circles, Springer (2004).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 428, 2014, pp. 182–195.
Translated by L. Yu. Kolotilina.
Rights and permissions
About this article
Cite this article
Kolotilina, L.Y. Bounds for the Inverses of Generalized Nekrasov Matrices. J Math Sci 207, 786–794 (2015). https://doi.org/10.1007/s10958-015-2401-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-015-2401-x