Correction to: A dual iterative substructuring method with a small penalty parameter

TL;DR

This paper corrects a previous work by providing a counterexample to a key inequality and offering a new proof for a lemma related to eigenvalue estimates in a dual operator, refining the theoretical foundation of the original method.

Contribution

It presents a correction to prior results by constructing a counterexample and supplying a new proof for an important lemma in the analysis of a dual operator in domain decomposition methods.

Findings

Counterexample to the strengthened Cauchy--Schwarz inequality

New proof for Lemma 5 with eigenvalue estimates

Refined theoretical understanding of the dual operator

Abstract

In this corrigendum, we offer a correction to [J. Korean. Math. Soc., 54 (2017), pp. 461--477]. We construct a counterexample for the strengthened Cauchy--Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.