2 research outputs found
Computing the square roots of matrices with central symmetry
For computing square roots of a nonsingular matrix A, which are functions of A, two well known fast and stable algorithms, which are
based on the Schur decomposition of A, were proposed by Bj¨ork and Hammarling
[3], for square roots of general complex matrices, and by Higham [10], for real square roots of real matrices. In this paper we further consider (the computation of) the square roots of matrices with central symmetry.
We first investigate the structure of the square roots of these matrices and
then develop several algorithms for computing the square roots. We show that our algorithms ensure significant savings in computational costs as compared to the use of standard algorithms for arbitrary matrices.Fundação para a Ciência e a Tecnologia (FCT
Structure-preserving Schur methods for computing square roots of real skew-Hamiltonian matrices
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.Comment: 27 pages; Conference "Directions in Matrix Theory 2011", July 2011,
University of Coimbra, Portuga