Search

The paper considers the classes of GSDD1, GSDD 1 ∗ , and SD-SDD matrices, which contain the class of SDD (strictly diagonally dominant) matrices and are contained in the class of nonsingular H -matrices. New upper bounds on ‖ A - 1 ‖ ∞ for GSDD1, GSDD 1 ∗ , and SD-SDD matrices A, generalizing known upper bounds for S-SDD, SDD 1 ∗ , and GSDD1 matrices, are established and compared. [ABSTRACT FROM AUTHOR]

The paper continues the study of block generalizations of Nekrasov matrices and introduces two new classes of the so-called G ˜ N and BJN matrices and compares them with the previously introduced class of GN matrices. Different properties of G ˜ N and BJN matrices are established. In particular, it is proved that the classes G ˜ N and {BJN} are closed with respect to Schur complements and monotone with respect to block partitioning. Also upper bounds for the norms ‖A−1‖∞ of inverses of GN, G ˜ N , and BJN matrices A are considered. General results obtained are specialized to the case of block two-by-two matrices with scalar first diagonal block. [ABSTRACT FROM AUTHOR]

The paper introduces the so-called generalized Nekrasov (GN) matrices, which provide a block extension of the ordinary Nekrasov matrices. Basic properties of GN matrices are studied. In particular, it is proved that the GN matrices form a subclass of nonsingular H-matrices and this subclass is closed with respect to Schur complements obtained by eliminating leading principal block submatrices. Also an upper bound for the l∞-norm of the inverse to a GN matrix, which generalizes the known bound for Nekrasov matrices, is obtained. The case of block two-by-two GN matrices with scalar first diagonal blocks, which prove to be Dashnic–Zusmanovich matrices of the first type, is considered separately. The bounds obtained are applied to SDD matrices. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The paper suggests generalizations of some known sufficient nonsingularity conditions for matrices with constant principal diagonal and the corresponding eigenvalue inclusion sets to the cases of arbitrary matrices and matrices with nonzero diagonal entries. Bibliography: 11 titles. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The paper suggests sufficient nonsingularity conditions for matrices in terms of certain determinantal relations of diagonal dominance type, which improve and generalize some known results. These conditions are used to describe new eigenvalue inclusion sets and to derive new two-sided bounds on the determinants of matrices satisfying them. Bibliography: 8 titles. [ABSTRACT FROM AUTHOR]