On the accuracy of the chemically significant eigenvalue method

We study the accuracy and convergence properties of the chemically significant eigenvalues method as proposed by Georgievskii et al. [J. Phys. Chem. A 117, 12146-12154 (2013)] and its close relative, dominant subspace truncation, for reduction of the energy-grained master equation. We formally derive the connection between both reduction techniques and provide hard error bounds for the accuracy of the latter which confirm the empirically excellent accuracy and convergence properties but also unveil practically relevant cases in which both methods are bound to fall short. We propose the use of balanced truncation as an effective alternative in these cases. (c) 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper examines the accuracy and convergence properties of the chemically significant eigenvalues method and its related dominant subspace truncation method in the energy-grained master equation. It proposes a viable alternative method for cases where the aforementioned methods may fall short.