Related papers: Software for Computing the Spheroidal Wave Functio…
We here calculate the series expansion of the T-matrix for a spheroidal particle in the small-size/long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a non-spherical…
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…
For fixed $W\in \big(0,\frac{1}{2}\big)$ and positive integer $N\geq 1,$ the discrete prolate spheroidal wave functions (DPSWFs), denoted by $U_{k,W}^N,$ $0\leq k\leq N-1$ form the set of the eigenfunctions of the positive and finite rank…
In this paper we show that the classical problem of frequency estimation can be formulated and solved efficiently in an empirical Bayesian framework by assigning a uniform a priori probability distribution to the unknown frequency. We…
Fast and accurate computations of the power spectrum of cosmic microwave background fluctuations are essential for comparing current and upcoming data sets with the large parameter space of viable cosmological models. The most efficient…
Time domain astronomy and the increasing number of exoplanet candidates call for reliable, robust, and automatic wavelength calibration. We present an algorithm for wavelength calibrating \'echelle spectrographs that uses order-by-order…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
We revisit the calculation of gravitational radiation through the use of Weyl scalars. We point out several possible problems arising from gauge and tetrad ambiguities and ways to address them. Our analysis indicates how, relatively simple…
We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…
The quantitative characterization of the microstructure of random heterogeneous media in $d$-dimensional Euclidean space $\mathbb{R}^d$ via a variety of $n$-point correlation functions is of great importance, since the respective infinite…
This paper presents an operational framework for the computation of the discretized solutions for relativistic equations of Klein-Gordon and Dirac type. The proposed method relies on the construction of an evolution-type operador from the…
Large scale parameter estimation problems are among some of the most computationally demanding problems in numerical analysis. An academic researcher's domain-specific knowledge often precludes that of software design, which results in…
Scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is the wave…
For a massive scalar field in a fixed Schwarzschild background, the radial wave equation obeyed by Fourier modes is first studied. After reducing such a radial wave equation to its normal form, we first study approximate solutions in the…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
This paper is devoted to the computation of capillary-gravity solitary waves of the irrotational incompressible Euler equations with free surface. The numerical study is a continuation of a previous work in several points: an alternative…
The asymptotic iteration method is applied, to calculate the angular spheroidal eigenvalues $\lambda^{m}_{\ell}(c)$ with arbitrary complex size parameter $c$. It is shown that, the obtained numerical results of $\lambda^{m}_{\ell}(c)$ are…
The paper presents a versatile library of quasi-analytic complex-valued wavelet packets (WPs) which originate from polynomial splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based orthonormal WPs…