Padé and Padé-type approximation for \(2\pi\)-periodic \(L^p\) functions (Q1840681)

The main contribution of the paper is the introduction of the notion of composed Padé-type approximants. That are Padé-type approximants for complex functions where the generating polynomial for the real and the imaginary part of the function can be different. Definition and convergence properties are addressed. This is subsequently applied to harmonic functions and \(L^p\) functions. Numerical examples and two applications are mentioned (acceleration of convergence and approximate computation of derivatives and integrals). Many results of the paper are formulated not just for Padé or Padé-type approximation, but are formulated in a more general context of rational interpolation (with prescribed poles). The paper has also a relatively long historical introduction on rational approximation and continued fractions.