Here we consider a numerical procedure to interpolate on matrix Lie groups. By using the exponential map and its (1, 1) diagonal Pade approximant, piecewice interpolants may be derived. The approach based on the Pade map has the advantage that the computation of exponentials and logarithms of matrices are reduced. We show that the updating technique proposed by Enright in [1] may be applied when a dense output is required. The application to the numerical solution of a system ODEs on matrix group and to a classical interpolation problem are reported. (C) 2001 Elsevier Science Ltd. All rights reserved.
Piecewise Interpolants on Matrix Lie Groups / Mastroserio, C.; Politi, T.. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - STAMPA. - 14:3(2001), pp. 333-340. [10.1016/S0893-9659(00)00158-0]
Piecewise Interpolants on Matrix Lie Groups
Politi, T.
2001-01-01
Abstract
Here we consider a numerical procedure to interpolate on matrix Lie groups. By using the exponential map and its (1, 1) diagonal Pade approximant, piecewice interpolants may be derived. The approach based on the Pade map has the advantage that the computation of exponentials and logarithms of matrices are reduced. We show that the updating technique proposed by Enright in [1] may be applied when a dense output is required. The application to the numerical solution of a system ODEs on matrix group and to a classical interpolation problem are reported. (C) 2001 Elsevier Science Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
