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Journal of Mathematical Sciences

, Volume 224, Issue 6, pp 911–925 | Cite as

New Subclasses of the Class of \( \mathrm{\mathscr{H}} \)-Matrices and Related Bounds for the Inverses

  • L. Yu. Kolotilina
Article

The paper introduces new subclasses, called P\( \mathrm{\mathscr{H}} \)N(π) and P\( \mathrm{\mathscr{H}} \)QN(π), of (nonsingular) \( \mathrm{\mathscr{H}} \)-matrices of order n dependent on a partition π of the index set {1, . . ., n}, which generalize the classes P\( \mathrm{\mathscr{H}} \)(π), introduced previously, and contain, in particular, such subclasses as those of strictly diagonally dominant (SDD), Nekrasov, S-SDD, S-Nekrasov, QN, and P\( \mathrm{\mathscr{H}} \)(π) matrices. Properties of the matrices introduced are studied, and upper bounds on their inverses in l norm are obtained. Block generalizations of the classes P\( \mathrm{\mathscr{H}} \)N(π) and P\( \mathrm{\mathscr{H}} \)QN(π) in the sense of Robert are considered.

Also a general approach to defining subclasses \( {\mathcal{K}}^{\pi } \) of the class \( \mathrm{\mathscr{H}} \) containing a given subclass \( \mathcal{K} \)\( \mathrm{\mathscr{H}} \) and dependent on a partition π is presented.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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