Higher Order Variational Principles and Padé Approximants for Linear Functionals

The relationship between higher order variational principles for linear functionals of the solution to an inhomogeneous equation and Padé approximants for the same functional is shown. This leads to a deeper understanding of these higher order principles. Further, it is noted that in certain cases, the Roussopoulos functional can yield divergent results while using the Ritz procedure, shown to be equivalent to forming Padé approximants for the functional of interest, gives a generalized Schwinger normalization independent variational principle that can yield finite and convergent results.