Dual Variational Principles and Padé-type Approximants

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Abstract
Families of approximants for <Ø, f> are derived from dual variational functionals associated with the linear equation (1+yL)Ø=f. Expansions in both ascending and descending powers of y are considered, and the approximants are identified either as one- or two-point Padé approximants, or as approximants of a closely related type. Compact formulae are obtained for the approximants, and their duality and bounding properties are exhibited. Attention is paid to the special situations occurring when the non-negative self-adjoint operator L (i) has a zero eigenvalue, (ii) is bounded.

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