Year: 2026
Type: preprint
Abstract: For a given matrix \( A \) in the real Schur form, the eigenvalue swapping algorithm is used to swap two adjacent diagonal blocks. In LAPACK, this operation is performed by the subroutine~\texttt{SLAEXC}/\texttt{DLAEXC}, which is based on a direct swapping algorithm proposed by Bai and Demmel in 1993. In this work, we present a thorough error analysis of a modified direct swapping algorithm. By a carefully designed pivoted Givens QR factorization, this algorithm can achieve an error bound of the form \( O( \boldsymbol{u} \lVert A \rVert ) \) under mild assumptions, where \( \boldsymbol{u} \) is the unit roundoff. We present empirical evidence to illustrate the superior stability of our algorithm over existing approaches.
Source: arXiv (Cornell University)
Authors: Shao, Meiyue, Xu, Rentao
Institution: Fudan University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223302609