Erratum to: Inexact constraint preconditioners for linear systems arising in interior point methods

Abstract

It was brought to our attention by Professor Valeria Simoncini that our proof of Theorem 2.1 [2, p. 139] is incorrect. Indeed, on page 140 we write the inequality (2.4) which is correct because we work with A which is an m× n matrix and m ≤ n and rank(A)=m hence ‖AT y‖ ‖y‖ ≥ σ1. However, on page 141 we write the inequality (2.6). We try to use a similar argument but now instead of A we have A and x ∈Rn. Hence the inequality ‖Ax‖ ‖x‖ ≥ σ1 (which we use to prove inequality (2.6)) is incorrect. In this short note we restate Theorem 2.1 of [2] and give a new proof.