Ay. Tsaune et Mp. Dyachenko, General scheme of splittings of degenerate eigensubspaces and eigenelements of self-adjoint operators in high orders of perturbation theory, J MATH PHYS, 41(8), 2000, pp. 5793-5813
The possibility of arbitrary alternation of splitting and nonsplitting orde
rs is taken into consideration through the idea of a stage of perturbation
theory. In every order an eigenvalue equation is to be solved; its effectiv
e operator is obtained by means of a unified scheme from the operator of th
e previous order. The complete aggregate of subspace splittings leads to th
e correct set of eigenvectors of zero approximation. Expressions of any ord
er corrections for the correct vectors leading to eigenvectors of a perturb
ed operator are obtained and discussed. (C) 2000 American Institute of Phys
ics. [S0022-2488(00)03504-0].