GENERALIZED RAYLEIGH QUOTIENTS FOR EIGENVALUE ESTIMATES OF NEUTRON BALANCE-EQUATIONS

Generalized Rayleigh quotients are developed to provide estimates of t he eigenvalues of the continuous-energy transport equation and its dif fusion approximation. The new variational principles extend the applic ability of the quotient to perturbations of the boundary as well as th e 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. T he correctness of the principles are verified by reproducing the first -order perturbation results and considering some numerical examples fo r the case of boundary perturbation.