Generalization of the Variational Method of Kahan, Rideau, and Roussopoulos and Its Application to Neutron Transport Theory

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Abstract
The variational method of Kahan, Rideau, and Roussopoulos (KRR) frequently used in neutron transport theory to estimate weighted averages is extended and generalized. In the KRR variational method a first variation in the trial functions produces a second variation in the estimate of the weighted average. Two generalized variational functionals which depend on trial operators instead of trial functions are given. A first variation in the trial operators produces an nth variation in the estimate of the weighted average when an nth order generalized variational functional is used. Both perturbation theory and the KRR variational method are derived as special cases of the generalized variational method. Several examples including calculations of transport equation spatial moments using diffusion equation solutions as trial operators are studied with good results.