Abstract
The class of generalized α-matrices is presented by Cvetković, L. (2006), and proved to be a subclass of H-matrices. In this paper, we present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H-matrix. Furthermore, using the generalized arithmetic-geometric mean inequality, we obtain two new classes of H-matrices. As applications of the obtained results, three regions including all the eigenvalues of a matrix are given.
Highlights
H-matrices play a very important role in Numerical Analysis, in Optimization theory and in other Applied Sciences [1]-[7]
The class of generalized α-matrices is presented by Cvetković, L. (2006), and proved to be a subclass of H-matrices
We present a new class of matrices-generalized irreducible α-matrices, and prove that a generalized irreducible α-matrix is an H-matrix
Summary
H-matrices play a very important role in Numerical Analysis, in Optimization theory and in other Applied Sciences [1]-[7]. By considering the irreducibility of a matrix, Taussky [14] [15] extended the notion of a strictly diagonally dominant matrix, and given the following subclass of H-matrices (see Definition 2). A matrix=A aij ∈ Cn×n is called an irreducibly diagonally dominant matrix if A is irreducible, if for any i ∈ N , aii ≥ ri ( A). A matrix=A aij ∈ Cn×n is called a generalized irreducible α-matrix if A is irreducible and if there exists α ∈[0,1] and k ∈ N such that for each subset S ⊆ N of cardinality k ( ) ( ) aii ≥ riS ( A) α ciS ( A) ( ) 1−α +riS A (5).
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