The paper considers some classes of block matrices that can be regarded as block generalizations of the class of \( \mathrm{\mathscr{H}} \)-matrices and interrelations among them. New bounds for the infinity norm of inverses for matrices in the classes under consideration are suggested.
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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 R. Varga, “A new Geršgorin-type eigenvalue inclusion area,” ETNA, 18, 73–80 (2004).
M. Fiedler and V. Ptak, “Generalized norms of matrices and the location of the spectrum,” Czech. Math. J., 12 (87), 558–571 (1962).
D. G. Feingold and R. S. Varga, “Block diagonally dominant matrices and generalization of the Gerschgorin circle theorem,” Pacific J. Math., 12, 1241–1250 (1962).
L. Yu. Kolotilina, “Improving Chistyakov’s bounds for the Perron root of a nonnegative matrix,” Zap. Nauchn. Semin. POMI, 346, 103–118 (2007).
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 inverses of PM- and PH-matrices,” Zap. Nauchn. Semin. POMI, 367, 75–109 (2009).
L. Yu. Kolotilina, “Diagonal dominance characterization of PM- and PH-matrices,” Zap. Nauchn. Semin. POMI, 367, 110–120 (2009).
L. Yu. Kolotilina, “Bounds for the infinity norm of the inverse for certain M- and Hmatrices,” Linear Algebra Appl., 430, 692–702 (2009).
L. Yu. Kolotilina, “Bounds on the l ∞ norm of inverses for certain block matrices,” Zap. Nauchn. Semin. POMI, 439, 145–158 (2015).
L. Yu. Kolotilina, “New subclasses of the class of \( \mathrm{\mathscr{H}} \)-matrices and related bounds for the inverses,” Zap. Nauchn. Semin. POMI, 453, 148–171 (2016).
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).
A. Ostrowski, “On some metrical properties of operator matrices and matrices partitioned into blocks,” J. Math. Anal. Appl., 2, 161–209 (1961).
B. Polman, “Incomplete blockwise factorizations of (Block) H-matrices,” Linear Algebra Appl., 90, 119–132 (1987).
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).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 453, 2016, pp. 172–188.
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Kolotilina, L.Y. On Block Generalizations of \( \mathrm{\mathscr{H}} \)-Matrices. J Math Sci 224, 926–936 (2017). https://doi.org/10.1007/s10958-017-3462-9
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DOI: https://doi.org/10.1007/s10958-017-3462-9