Upper-Bound Estimation of Bilinear Functionals in Reactor Theory

Expressions for estimating upper bounds to integral parameters of the form 〈W, Kψ/〈W, ψ〉 are derived using functional analysis techniques. The resulting formulations are applied for estimating upper bounds to different types of integral parameters in reactor theory, including direct eigenvalues of the Boltzmann equation, reactivity, and effective reactor kinetics parameters. The upper-bound estimation method is compared with perturbation theory techniques for estimating changes in the total collision eigenvalue.