Newton Method for Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
M. Joho · SIAM Journal on Matrix Analysis and Applications · 2008
In this paper we present a Newton method to jointly approximately diagonalize a set of positive definite Hermitian matrices. To this end, we derive the local gradient and Hessian of the underlying cost function in closed form. The algorithm is derived for the complex case and can also update a nonsquare diagonalization matrix. We analyze the cost function at the critical points and show its relation to a different cost function that is commonly studied.