Improvements on the infinity norm bound for the inverse of Nekrasov matrices

TL;DR

This paper presents new parameterized bounds for estimating the infinity norm of the inverse of Nekrasov matrices, improving upon previous bounds and demonstrating their effectiveness through numerical examples.

Contribution

Introduces optimized bounds involving a parameter for the inverse of Nekrasov matrices, surpassing earlier bounds by Cvetkovic et al. (2013).

Findings

New bounds are tighter than previous estimates.

Optimal parameter values improve bound accuracy.

Numerical examples confirm the theoretical improvements.

Abstract

We focus on the estimating problem of the infinity norm of the inverse of Nekrasov matrices, give new bounds which involve a parameter, and then determine the optimal value of the parameter such that the new bounds are better than those in L. Cvetkovic et al. (2013). Numerical examples are given to illustrate the corresponding results.