Related papers: Pad\'e approximants for truncated post-Newtonian n…
We propose a novel approach for parameterizing the luminosity distance, based on the use of rational "Pad\'e" approximations. This new technique extends standard Taylor treatments, overcoming possible convergence issues at high redshifts…
We test the resummation techniques used in developing Pad\'e and Effective One Body (EOB) waveforms for gravitational wave detection. Convergence tests show that Pad\'e approximants of the gravitational wave energy flux do not accelerate…
In transferring some results from universal Taylor series to the case of Pad\'e approximants we obtain stronger results, such as, universal approximation on compact sets of arbitrary connectivity and generic results on planar domains of any…
The luminosity distance in the standard cosmology as given by $\Lambda$CDM and consequently the distance modulus for supernovae can be defined by the Pad\'e approximant. A comparison with a known analytical solution shows that the Pad\'e…
As a preliminary step towards simulating binary neutron star coalescing problem, we test a post-Newtonian approach by constructing a single neutron star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic equilibrium by…
Cosmography is used in cosmological data processing in order to constrain the kinematics of the universe in a model-independent way, providing an objective means to evaluate the agreement of a model with observations. In this paper, we…
We introduce a method to obtain self-consistent, axially symmetric, thin disklike stellar models in the first post-Newtonian (1PN) approximation. The models obtained are fully analytical and corresponds to the post-Newtonian generalizations…
Next-generation gravitational-wave detectors are expected to constrain the properties of extreme density matter via observations of static and dynamical tides in binary neutron star inspirals. The required modelling is straightforward in…
Cosmography becomes non-predictive when cosmic data span beyond the red shift limit $z\simeq1 $. This leads to a \emph{strong convergence issue} that jeopardizes its viability. In this work, we critically compare the two main solutions of…
Standard puncture initial data have been widely used for numerical binary black hole evolutions despite their shortcomings, most notably the inherent lack of gravitational radiation at the initial time that is later followed by a burst of…
Pad$\acute{e}$ cosmography has been widely used to probe the cosmic evolution and to investigate the nature of dark energy. In this paper, we find that the Pad$\acute{e}$ approximant can describe the cosmic evolution better than the…
Reliable predictions of general relativity theory are extracted using approximation methods. Among these, the powerful post-Newtonian approximation provides us with our best insights into the problems of motion and gravitational radiation…
We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power…
Recently it has been pointed out that diagonal Pad\'e approximants to truncated perturbative series in gauge theories have the remarkable property of being independent of the choice of the renormalization scale as long as the gauge coupling…
Methods of Pad\'e approximation are used to analyse a multivariate Markov transform which has been recently introduced by the authors, and which is generalizing the well-known in Spectral theory Stieltjes transform (Markov function) of…
As is well known, in mathematics, any function could be approximated by the Pad\'e approximant. The Pad\'e approximant is the best approximation of a function by a rational function of given order. In fact, the Pad\'e approximant often…
We develop a "hybrid approximative scheme" in the framework of the post-Newtonian approximation for computing general-relativistic polytropic models simulating neutron stars in critical rigid rotation. We treat the differential equations…
The advantages and difficulties of application of Pad\'e approximants to two-dimensional regression analysis are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations…
Among several analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate scheme is known to be unusually accurate even in mildly non-linear regime. This…
We establish properties concerning the distribution of poles of Pad e approximants, which are generic in Baire category sense. We also investigate Pad e universal series, an analog of classical universal series, where Taylor partial sums…