The Parallel Algorithm of the Regularized Lions' Decomposition Method for Solving the Full Problem on Eigenvalues and Eigenvectors

L.A. Sevastianov, A.V. Zorin

PFUR, Moscow, Russia

In the quantum mechanics with a non-negative quantum distribution function operators for observable objects differ from operators, used in the orthodox quantum mechanics, by some non-small perturbation. Thus perturbed degenerate discrete spectrum of the old Hamiltonian splits in series of close eigenvalues of the new Hamiltonian operator. The problem of calculating of these eigenvalues and corresponding eigenvectors by the Rayleigh-Ritz method in the basis of eigenvectors of the Hamiltonian operator is the unstable ill-conditioned problem. We solve the full problem on close or multiple eigenvalues and eigenvectors of a finite dimensional Hamiltonian operator, appearing in the Rayleigh-Ritz method, by an exact penalty function method reducing it to the problem of searching the Nash point by modified Lions' decomposition method. The last problem may be solved using a parallel calculations algorithm.