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We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…
The goal of the present paper is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
When a laser passes through underdense plasmas, Raman and Brillouin Backscattering can reflect a substantial portion of the incident laser energy. This is a major loss mechanism, for example, in employing lasers in inertial confinement…
A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…
We propose a new method to analyse the alignment of optical polarisation vectors from quasars. This method leads to a definition of intrinsic preferred axes and to a determination of the probability $p^{\sigma}$ that the distribution of…
We propose and investigate two new methods to approximate $f({\bf A}){\bf b}$ for large, sparse, Hermitian matrices ${\bf A}$. The main idea behind both methods is to first estimate the spectral density of ${\bf A}$, and then find…
In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple independent observations. Of…
The angle of rotation of any target about the radar line of sight (LOS) is known as the polarization orientation angle. The orientation angle is found to be non-zero for undulating terrains and man-made targets oriented away from the radar…
The effect of an intense external linear polarized radiation field on the angular distributions and polarization states of the photons emitted during the radiative recombination is investigated. It is predicted, on symmetry grounds, and…
Chebychev approximations are given for the Gamma and the Polygamma functions in only one contiguous intervall [1..inf] with a definable maximal relative error. The approximations need about three coefficients per decimal until a checked…
Single-parameter summaries of variable effects in regression settings are desirable for ease of interpretation. However (partially) linear models for example, which would deliver these, may fit poorly to the data. On the other hand, an…
Polynomial reproduction plays a relevant role in deriving error estimates for various approximation schemes. Local reproduction in a quasi-uniform setting is a significant factor in the estimation of error and the assessment of stability…
Polarimetry is about to become a powerful tool for determining the atmospheric properties of exoplanets. To provide the basis for the interpretation of observational results and for predictive studies to guide future observations,…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
We have developed a complete theory for the calculation of the observed Stokes parameters for radiation emitted from the surface of a rapidly rotating neutron star (NS) using the oblate Schwarzschild approximation. We accounted for the…
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix…
We study the polarization properties of 22 known rotating radio transients (RRATs) with the 64-m Parkes radio telescope and present the Faraday rotation measures (RMs) for the 17 with linearly polarized flux exceeding the off-pulse noise by…
We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…
The radio polarization properties of the pulsar population are only superficially captured by the conventional picture of pulsar radio emission. We study the broadband polarization of 271 young radio pulsars, focusing particularly on…