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Research Article | Open Access

Infinity norm upper bounds for the inverse of S D D 1 matrices

Xiaoyong Chen, Yating Li, Liang Liu, Yaqiang Wang( )
School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi, 721013, China
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Abstract

In this paper, a new proof that S D D 1 matrices is a subclass of H-matrices is presented, and some properties of S D D 1 matrices are obtained. Based on the new proof, some upper bounds of the infinity norm of inverse of S D D 1 matrices and S D D matrices are given. Moreover, we show that these new bounds of S D D matrices are better than the well-known Varah bound for S D D matrices in some cases. In addition, some numerical examples are given to illustrate the corresponding results.

Keywords

SDD1 matricesSDD matricesupper boundpositive diagonal matrixinfinity norm
CLC number: 15A15, 15A48, 65F05, 65F40

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8847-8860
DOI: 10.3934/math.2022493

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Cite this article:
Chen X, Li Y, Liu L, et al. Infinity norm upper bounds for the inverse of S D D 1 matrices. AIMS Mathematics, 2022, 7(5): 8847-8860. https://doi.org/10.3934/math.2022493

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Received: 10 August 2021
Revised: 21 February 2022
Accepted: 25 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)