Variational functionals are presented which provide an estimate of ratios of linear and bilinear functionals of the solutions of the direct and adjoint equations (inhomogeneous and homogeneous) governing linear systems. These variational functionals are used as the basis for a generalized perturbation theory for estimating the effects of changes in system parameters upon these ratios of linear and bilinear functionals. The relation of the present theory to the variational theory of Pomraning and to the generalized perturbation theory of Usachev and Gandini is discussed. Potential applications of the theory to nuclear reactor physics are outlined.
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We shall speak of an “equation” throughout. However, the formalism is appropriate for matrix operations as well and, hence, is applicable to systems of equations.
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© 1972 The American Institute of Physics.
1972
The American Institute of Physics
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