Variational approach to the solution of linear multiparameter eigenvalue problems - Podlevs’kyi, B. M. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
We associate a multiparameter spectral problem in a real Euclidean space with a variational problem of finding a minimum of a certain functional. We establish the equivalence of the spectralproblem and the variational problem. On the basis of the gradient procedure, we propose a numerical algorithm for the determination of its eigenvalues and eigenvectors. The local convergence of the algorithm is proved.