Volume 55, pp. 455-468, 2022.

Structured shifts for skew-symmetric matrices

Chen Greif


We consider the use of a skew-symmetric block-diagonal matrix as a structured shift. Properties of Hamiltonian and skew-Hamiltonian matrices are used to show that the shift can be effectively used in the iterative solution of skew-symmetric linear systems or nonsymmetric linear systems with a dominant skew-symmetric part. Eigenvalue analysis and some numerical experiments confirm our observations.

Full Text (PDF) [293 KB], BibTeX

Key words

skew-symmetric matrix, structured shift, Hamiltonian matrix, skew-Hamiltonian matrix, eigenvalue analysis, iterative solution of linear systems

AMS subject classifications

65F08, 65F10, 65F50, 15A12, 15B57

Links to the cited ETNA articles

[6]Vol. 11 (2000), pp. 85-93 Peter Benner, Ralph Byers, Heike Fassbender, Volker Mehrmann, and David Watkins: Cholesky-like factorizations of skew-symmetric matrices
[10]Vol. 8 (1999), pp. 115-126 Peter Benner, Volker Mehrmann, and Hongguo Xu: A note on the numerical solution of complex Hamiltonian and skew-Hamiltonian eigenvalue problems
[23]Vol. 54 (2021), pp. 370-391 Murat Manguoğlu and Volker Mehrmann: A two-level iterative scheme for general sparse linear systems based on approximate skew-symmetrizers

ETNA articles which cite this article

Vol. 58 (2023), pp. 84-100 Fang Chen and Bi-Cong Ren: A modified alternating positive semidefinite splitting preconditioner for block three-by-three saddle point problems

< Back