Structure-preserving Schur methods for computing square roots of real skew-Hamiltonian matrices

TL;DR

This paper characterizes all square roots of real skew-Hamiltonian matrices and introduces a structure-preserving method that is more efficient than standard approaches for computing these roots.

Contribution

It provides a complete characterization of square roots of real skew-Hamiltonian matrices and proposes a structure-preserving computational method that reduces arithmetic complexity.

Findings

Complete characterization of square roots of real skew-Hamiltonian matrices

Proposed structure-preserving method requires less arithmetic

Method outperforms standard real Schur method in efficiency

Abstract

Our contribution is two-folded. First, starting from the known fact that every real skew-Hamiltonian matrix has a real Hamiltonian square root, we give a complete characterization of the square roots of a real skew-Hamiltonian matrix W. Second, we propose a structure exploiting method for computing square roots of W. Compared to the standard real Schur method, which ignores the structure, our method requires significantly less arithmetic.