Convergence estimates for the Magnus expansion IIA. $2\times2$ matrices with operator norm
Spectral Theory
2023-04-10 v1 Classical Analysis and ODEs
Abstract
We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff expansion are also made. In this Part IIA, we investigate the case of matrices with respect to the operator norm. We consider norm estimates and minimal presentations in terms of the Magnus and BCH expansions. Some results are obtained in the complex case, but a more complete picture is obtained in the real case.
Keywords
Cite
@article{arxiv.2304.03513,
title = {Convergence estimates for the Magnus expansion IIA. $2\times2$ matrices with operator norm},
author = {Gyula Lakos},
journal= {arXiv preprint arXiv:2304.03513},
year = {2023}
}
Comments
Part II/2 of original submission arXiv:1709.01791, expanded. arXiv admin note: text overlap with arXiv:1910.03328