The constrained newton method on a Lie group and the symmetric eigenvalue problem Original Research Article

The Newton method for estimating a critical point of a real function is formulated in a coordinate free manner on an arbitrary Lie group. Convergence proofs for the numerical method are given. An application of the general approach to computing the eigenvalues of a symmetric matrix is given, and the resultant algorithm is compared with the classical shifted QR algorithm. Properties of the method described suggest that it is of interest for certain computations in online and adaptive environments.