Ineffectiveness of Padé resummation techniques in post-Newtonian approximations

Post-Newtonian approximations

After a very basic introduction about the geometric view of gravitation, we deal with Newtonian and post-Newtonian approximations giving an overview of the parametrized post-Newtonian formalism. In the final part, we focus on the classical experimental tests. This is a bibliographic work in which an effort has been made to explore the historical timeline and motivation, managing the original re...

Three-body equations of motion in successive post-newtonian approximations

Post-newtonian Approximations and Equations of Motion of General Relativity

A post-Newtonian approximation scheme for general relativity is defined using the Arnowitt-Deser-Misner formalism. The scheme is applied to perfect fluids and point-mass systems. The two-body point-mass Hamiltonian is given explicitly up to the post2.5-Newtonian order.

An operator approach to multipoint Padé approximations

First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the NevanlinnaPick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations c...

A-stable Padé approximations and quadratic stability

In this paper we prove that all A-stable Padé approximations for the matrix exponential preserve common quadratic Lyapunov functions for switched linear systems.