Swapping 2 × 2 blocks in the Schur and generalized Schur form

Camps, Daan; Mastronardi, Nicola; Vandebril, Raf; Van Dooren, Paul; Camps, Daan

doi:10.1016/j.cam.2019.05.022

Swapping 2 × 2 blocks in the Schur and generalized Schur form

Author:

Camps, Daan

Mastronardi, Nicola ; Vandebril, Raf ; Van Dooren, Paul ; Camps, Daan

Keywords:

Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Eigenvalues, Schur form, Reordering Schur form, Stability, C14/16/056#53765160, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 0906 Electrical and Electronic Engineering, Numerical & Computational Mathematics, 4613 Theory of computation, 4901 Applied mathematics, 4903 Numerical and computational mathematics

Abstract:

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.