Abstract
Based on the Schur complement, some upper bounds for the infinity norm of the inverse of generalized doubly strictly diagonally dominant matrices are obtained. In addition, it is shown that the new bound improves the previous bounds. Numerical examples are given to illustrate our results. By using the infinity norm bound, a lower bound for the smallest singular value is given.
Highlights
Throughout the paper, let n be an integer number, N := {1, 2, . . . , n} be the set of all indices, Cn×n denote the set of all n × n complex matrices, I ∈ Rn×n j=n be an identity matrix, |A| = [|aij|] ∈ Rn×n, ri(A) := ∑ |aij| denote deleted ith row sum, j=1,j=i and J := {i ∈ N : |aii| > ri(A)}.Citation: Li, Y.; Wang, Y
In this paper, based on the Schur complement, we present some upper bounds for the infinity norm of the inverse of generalized doubly strictly diagonally dominant (GDSDD) matrices, and numerical examples are given to show the effectiveness of the obtained results
We prove that the bound in Theorem 9 generally improves the bound obtained by Theorem 3 in [11] for strictly diagonally dominant (SDD) matrices and Theorem 9 in [12] for doubly strictly diagonally dominant (DSDD) matrices
Summary
In 2020, based on the Schur complement, Li [11] obtained two upper bounds for the infinity norm of inverse of SDD matrices. In this paper, based on the Schur complement, we present some upper bounds for the infinity norm of the inverse of GDSDD matrices, and numerical examples are given to show the effectiveness of the obtained results. Applying these new bounds, a lower bound for the smallest singular value of GDSDD matrices is obtained
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