An Algorithm to Compute Averages on Matrix Lie Groups

Averaging is a common way to alleviate errors and random fluctuations in measurements and to smooth out data. Averaging also provides a way to merge structured data in a smooth manner. The present paper describes an algorithm to compute averages on matrix Lie groups. In particular, we discuss the case of averaging over the special orthogonal group of matrices, the unitary group of matrices and the group of symmetric positive-definite matrices.