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New Subclasses of the Class of $$ \mathrm{\mathscr{H}} $$ -Matrices and Related Bounds for the Inverses.
- Source :
-
Journal of Mathematical Sciences . Aug2017, Vol. 224 Issue 6, p911-925. 15p. - Publication Year :
- 2017
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 224
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 123904997
- Full Text :
- https://doi.org/10.1007/s10958-017-3461-x