A General Modal-Expansion Method for Obtaining Approximate Equations for Linear Systems

A general method for replacing a rigorous equation by a set of approximate equations with a reduced number of independent variables is presented. The modal-expansion method includes, as special cases, many of the techniques employed in reactor-physics calculations: harmonic analysis, polynomial expansions, semi-direct variational methods, weighted-residual methods, region balance, etc. The mathematical significance of the procedure is discussed in terms of the representation of a linear operator equation on a linear vector space. The concept of a “best” set of approximate equations is examined with respect to certain error criteria.