A new algorithm for the generalized eigenvalue problem
Knut Hüper, Uwe Helmke · 2002
The problem of finding the generalized eigenvalues and eigenvectors of a pair of real symmetric matrices A and B, with B>0, can be viewed as a smooth optimization problem on a smooth manifold. We present a cost function approach to the generalized eigenvalue problem which is posed on the product of the n-sphere and Euclidian space R. The critical point set of this cost function is studied. An algorithm is presented based on constrained optimization. A proof of local quadratic convergence is given.