The paper suggests upper bounds for the l ∞ norm of the inverses to block matrices belonging to certain subclasses of the class of block \( \mathrm{\mathscr{H}} \)-matrices, which improve and supplement known results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
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 and K. Doroslovački, “Max norm estimation for the inverse of block matrices,” Appl. Math. Comput., 242, 694–706 (2014).
L. Cvetković, V. Kostić, and K. Doroslovački, “Max-norm bounds for the inverse of S-Nekrasov 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).
D. G. Feingold and R. S. Varga, “Block diagonally dominant matrices and generalization of the Gerschgorin circle theorem,” Pacific J. Math., 12, 1241–1249 (1962).
L. Yu. Kolotilina, “Bounds for the determinants and inverses of certain H-matrices,” Zap. Nauchn. Semin. POMI, 346, 81–102 (2007).
L. Yu. Kolotilina, “Bounds for the infinity norm of the inverse for certain M- and H-matrices,” Linear Algebra Appl., 430, 692–702 (2009).
L. Yu. Kolotilina, “On bounding inverses to Nekrasov matrices in the infinity norm,” Zap. Nauchn. Semin. POMI, 419, 111–120 (2013).
L. Yu. Kolotilina, “Bounds for the inverses of generalized Nekrasov matrices,” Zap. Nauchn. Semin. POMI, 428, 182–195 (2014).
N. Morača, “Upper bounds for the infinity norm of the inverse of SDD and \( \mathcal{S} \) − SDD matrices,” J. Comput. Appl. Math., 206, 666–678 (2007).
F. Robert, “Blocs-H-matrices et convergence des méthodes itérative classiques par blocs,” Linear Algebra Appl., 2, 223–265 (1969).
E. Šanca and V. Kostić, “Diagonal scaling of a special type and its benefits,” Proc. Appl. Math. Mech., 13, 409–410 (2013).
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. 439, 2015, pp. 145–158.
Rights and permissions
About this article
Cite this article
Kolotilina, L.Y. Bounds on the l ∞ Norm of Inverses for Certain Block Matrices. J Math Sci 216, 816–824 (2016). https://doi.org/10.1007/s10958-016-2947-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-016-2947-2