In this paper we describe how to swap two 2 × 2 blocks in a real Schur form and a generalized real Schur form. We pay special attention to the numerical stability of the method. We also illustrate the stability of our approach by a series of numerical tests.
Camps, D., Mastronardi, N., Vandebril, R., & Van Dooren, P. (2019). Swapping 2 × 2 blocks in the Schur and generalized Schur form. Journal of Computational and Applied Mathematics. Accepted/in-press. https://doi.org/10.1016/j.cam.2019.05.022 (Original work published 2019)