Comments on "Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection"

TL;DR

This paper critically evaluates a previous work on decentralized subspace projection, providing counterexamples, corrections, and highlighting fundamental flaws in the original approach based on Schur decomposition.

Contribution

It dissects and refutes the main results of the prior paper, offering corrections and demonstrating the limitations of the proposed method.

Findings

Main results are disproved with counterexamples

Schur decomposition approach is ineffective for the problem

Most flaws in the original method cannot be remedied

Abstract

This correspondence disproves the main results in the paper "Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection" by S. Mollaebrahim and B. Beferull-Lozano. Counterexamples and counterproofs are provided when applicable. A correction is suggested for some of the flaws. However, it does not seem possible to amend most of the flaws since the overall approach based on a Schur decomposition of the shift matrix does not appear to be helpful to solve the desired problem.