# How to Compute Spectra with Error Control.

@article{Colbrook2019HowTC,
title={How to Compute Spectra with Error Control.},
author={Matthew J. Colbrook and Bogdan Roman and Anders C. Hansen},
journal={Physical review letters},
year={2019},
volume={122 25},
pages={
250201
}
}
• Published 28 June 2019
• Physics, Computer Science
• Physical review letters
Computing the spectra of operators is a fundamental problem in the sciences, with wide-ranging applications in condensed-matter physics, quantum mechanics and chemistry, statistical mechanics, etc. While there are algorithms that in certain cases converge to the spectrum, no general procedure is known that (a) always converges, (b) provides bounds on the errors of approximation, and (c) provides approximate eigenvectors. This may lead to incorrect simulations. It has been an open problem since…
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