Computation of functions of Hamiltonian and skew-symmetric matrices

N. Del Buono, L. Lopez and T. Politi

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 4, 1284-1297

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.

Keywords: Hamiltonian matrices; Skew-symmetric matrices; Matrix functions (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:4:p:1284-1297

DOI: 10.1016/j.matcom.2008.03.011

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