Critical Point Analysis of Joint Diagonalization Criteria

The stability and sensitivity of joint diagonalization criteria are analyzed using the Hessian of the criteria at their critical points. The sensitivity of some known joint diagonalization criteria is shown to be weak when they are applied to the matrices with closely placed eigenvalues. In such a situation, a large deviation in the diagonalizer cause a slight change in the criterion which makes the estimation of the diagonalizer difficult. To overcome the problem, a new joint diagonalization criterion is introduced. The criterion is linear with respect to the target matrices and has ability to cancel the effect of closely placed eigenvalues.