Abstract
By applying the properties of Schur complement and some inequality techniques, some new estimates of diagonally and doubly diagonally dominant degree of the Schur complement of Ostrowski matrix are obtained, which improve the main results of Liu and Zhang (2005) and Liu et al. (2012). As an application, we present new inclusion regions for eigenvalues of the Schur complement of Ostrowski matrix. In addition, a new upper bound for the infinity norm on the inverse of the Schur complement of Ostrowski matrix is given. Finally, we give numerical examples to illustrate the theory results.
Highlights
IntroductionIs called the Schur complement of A with respect to A(β)
Let Cn×n denote the set of all n × n complex matrices, N = {1, 2, . . . , n}, and A = ∈ Cn×n(n ≥ 2)
We present new inclusion regions for eigenvalues of the Schur complement of Ostrowski matrix
Summary
Is called the Schur complement of A with respect to A(β). A is an M-matrix, the Schur complement of A is an M-matrix and det A > 0 (see [3]). It is well known that the Schur complements of SDn and OSn are SDn and OSn, respectively. These properties have been used for the derivation of matrix inequalities in matrix analysis and for the convergence of iterations in numerical analysis (see [16,17,18,19]).
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