Piecewise interpolants on matrix lie groups

Abstract

Here we consider a numerical procedure to interpolate on matrix Lie groups. By using the exponential map and its (1, 1) diagonal Padé approximant, piecewice interpolants may be derived. The approach based on the Padé 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.