Related papers: Fast and accurate approximation of the angle-avera…
Radiative transfer modeling of spectral lines including partial redistribution (PRD) effects requires the evaluation of the ratio of the emission to the absorption profile. This quantity requires a large amount of computational work if one…
Aims. The main goal of this paper is to present an accurate and efficient numerical strategy for solving the radiative transfer problem for polarised radiation in strong resonance lines forming out of local thermodynamic equilibrium, taking…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
This paper proposes a Chebyshev polynomial expansion framework for the recovery of a continuous angular power spectrum (APS) from channel covariance. By exploiting the orthogonality of Chebyshev polynomials in a transformed domain, we…
Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to…
We present a generalized frequency redistribution function for the polarized two-term atom in an arbitrary magnetic field. This result is derived within a new formulation of the quantum problem of coherent scattering of polarized radiation…
Approximated forms of the RII and RIII redistribution matrices are frequently applied to simplify the numerical solution of the radiative transfer problem for polarized radiation, taking partial frequency redistribution (PRD) effects into…
We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…
A new method of antenna radiation pattern reconstruction using Chebyshev polynomials was presented in this paper. The analysis starts from the data measured in the frequency domain, and it corresponds to a direct propagating between two…
We present a fast method for estimating the cosmic microwave background polarization power spectra using unbiased estimates of heuristically-weighted correlation functions. This extends the O(N_pix^(3/2)) method of Szapudi et al. (2001) to…
Context. The correct modeling of the scattering polarization signals observed in several strong resonance lines requires taking partial frequency redistribution (PRD) phenomena into account. Aims. This work aims at assessing the impact and…
Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…
High precision polarization measurements open new opportunities for the study of the magnetic field structure as traced by polarimetric measurements of the interstellar dust emission. Polarization parameters suffer from bias in the presence…
In this paper we consider an orthonormal basis, generated by a tensor product of Fourier basis functions, half period cosine basis functions, and the Chebyshev basis functions. We deal with the approximation problem in high dimensions…
Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…
A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands…
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…
In this article we propose a numerical algorithm to compute the intensity and polarization of a polychromatic electromagnetic radiation crossing a medium with graded refractive index and modeled by the Vector Radiative Refractive Transfer…
This paper presents a detailed study of the scattering polarization profiles formed under partial frequency redistribution (PRD) in two thermal models of the solar atmosphere. Particular attention is given to understanding the influence of…
Context. Magnetic fields are important to the dynamics of many astrophysical processes and can typically be studied through polarization observations. Polarimetric interferometry capabilities of modern (sub)millimeter telescope facilities…