A note on non-inclusion "interval" root solvers

TL;DR

This paper critiques recent interval extension methods for solving nonlinear equations, highlighting that they lack the crucial inclusion property that characterizes genuine interval methods.

Contribution

It provides critical comments on faulty interval methods claiming to be self-validated, emphasizing the importance of the inclusion property.

Findings

Recent interval methods lack the essential inclusion property.

Faulty methods are published in multiple scientific journals.

Genuine interval methods must possess the inclusion property.

Abstract

In this note we give comments on recent interval extensions of the King-Ostrowski multipoint methods for solving nonlinear equations published in at least five scientific journals offering faulty "self-validated" methods. We show that they do not possess essential feature of genuine interval methods -- inclusion property.