Related papers: Applying Wirtinger derivatives to the radio interf…
Context: Radio interferometers measure frequency components of the sky brightness, modulated by the gains of the individual radio antennas. Due to atmospheric turbulence and variations in the operational conditions of the antennas these…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
New generation of radio interferometers are envisaged to produce high quality, high dynamic range Stokes images of the observed sky from the corresponding under-sampled Fourier domain measurements. In practice, these measurements are…
A new method for absolute polarimetric calibration of large telescopes is presented. The proposed method is highly accurate and is based on the calibration of a small sub-aperture, which is then extended to the full system by means of…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
This paper summarizes some of the major calibration and image reconstruction techniques used in radio interferometry and describes them in a common mathematical framework. The use of this framework has a number of benefits, ranging from…
The state of polarization and the carrier phase drift dynamically during transmission in a random fashion in coherent optical fiber communications. The typical digital signal processing solution to mitigate these impairments consists of two…
An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics:…
Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…
Direction-dependent instrumental polarisation introduces wide-field polarimetric aberrations and limits the dynamic range of low-frequency interferometric images. We therefore provide a detailed two-dimensional analysis of the Giant…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t.…
In this paper we propose and analyze a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel $(x-s)^{-\mu},0<\mu<1$. First we develop a family of fractional Jacobi…
Calibration of a typical radio interferometric array yields thousands of parameters as solutions. These solutions contain valuable information about the systematic errors in the data (ionosphere and beam shape). This information could be…
Interferometric calibration always yields non unique solutions. It is therefore essential to remove these ambiguities before the solutions could be used in any further modeling of the sky, the instrument or propagation effects such as the…
The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to…
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadrature rules. Our approach is based on the well-known fact that…
Radio Interferometry is an essential method for astronomical observations. Self-calibration techniques have increased the quality of the radio astronomical observations (and hence the science) by orders of magnitude. Recently, there is a…
In this work, exact solutions of the nonlinear cubic-quintic Duffing-van der Pol oscillator with variable coefficients are obtained. Two approaches have been applied, one based on the factorization method combined with the Field Method, and…
Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…