Generalized Rayleigh Quotients for Eigenvalue Estimates of Neutron Balance Equations

Generalized Rayleigh quotients are developed to provide estimates of the eigenvalues of the continuous-energy transport equation and its diffusion approximation. The new variational principles extend the applicability of the quotient to perturbations of the boundary as well as the boundary condition of the system. As a result, all three (operator, boundary condition, and external boundary) perturbation types can now be treated simultaneously, and the standard Rayleigh quotient appears as a special case of the variational principles given in this paper. The correctness of the principles are verified by reproducing the first-order perturbation results and considering some numerical examples for the case of boundary perturbation.