In this paper we consider numerical methods for computing functions of matrices being Hamiltonian and skew-symmetric. Analytic functions of this kind of matrices (i.e., exponential and rational functions) appear in the numerical solutions of ortho-symplectic matrix differential systems when geometric integrators are involved. The main idea underlying the presented techniques is to exploit the special block structure of a Hamiltonian and skew-symmetric matrix to gain a cheaper computation of the functions. First, we will consider an approach based on the numerical solution of structured linear systems and then another one based on the Schur decomposition of the matrix. Splitting techniques are also considered in order to reduce the computational cost. Several numerical tests and comparison examples are shown.

Computation of Functions of Hamiltonian and Skew-Hermitian Matrices / Del Buono, N.; Lopez, L.; Politi, Tiziano. - In: MATHEMATICS AND COMPUTERS IN SIMULATION. - ISSN 0378-4754. - 79:4(2008), pp. 1284-1297. [10.1016/j.matcom.2008.03.011]

Computation of Functions of Hamiltonian and Skew-Hermitian Matrices

POLITI, Tiziano
2008-01-01

Abstract

In this paper we consider numerical methods for computing functions of matrices being Hamiltonian and skew-symmetric. Analytic functions of this kind of matrices (i.e., exponential and rational functions) appear in the numerical solutions of ortho-symplectic matrix differential systems when geometric integrators are involved. The main idea underlying the presented techniques is to exploit the special block structure of a Hamiltonian and skew-symmetric matrix to gain a cheaper computation of the functions. First, we will consider an approach based on the numerical solution of structured linear systems and then another one based on the Schur decomposition of the matrix. Splitting techniques are also considered in order to reduce the computational cost. Several numerical tests and comparison examples are shown.
2008
Computation of Functions of Hamiltonian and Skew-Hermitian Matrices / Del Buono, N.; Lopez, L.; Politi, Tiziano. - In: MATHEMATICS AND COMPUTERS IN SIMULATION. - ISSN 0378-4754. - 79:4(2008), pp. 1284-1297. [10.1016/j.matcom.2008.03.011]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/5517
Citazioni
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 11
social impact