Related papers: Multivariate Anisotropic Interpolation on the Toru…
Context. The emergence of mixed modes during the subgiant phase, whose frequencies are characterized by a fast evolution with age, can potentially enable a precise determination of stellar properties, a key goal for future missions like…
We discuss the error analysis of linear interpolation on triangular elements. We claim that the circumradius condition is more essential then the well-known maximum angle condition for convergence of the finite element method. Numerical…
The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of…
In laser gravitational waves detectors optical loss restricts sensitivity. We discuss polarization scattering as one more possible mechanism of optical losses. Circulated inside interferometer light is polarized and after reflection its…
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
Primordial quantum fluctuations produced by inflation are conventionally assumed to be statistically homogeneous, a consequence of translational invariance. In this paper we quantify the potentially observable effects of a small violation…
In this paper we consider the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
With ever increasing availability of terahertz fields, it is important to find suitable detection techniques without compromising the measured dynamic range. Electro-optic terahertz sampling techniques, which are commonly used to detect…
A new error bound which is better than the current exponential-type error bound is presented in this paper.
Uniform LBB conditions are desirable to approximate the solution of Navier-Stokes, Oseen, and Stokes equations on anisotropic meshes and to enable anisotropic refinements. We prove such conditions for the second order Taylor-Hood pairs…
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…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…
We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prove that both the interpolants and their generalization errors…
We study oscillations of accretion torus with azimuthal magnetic field. For several lowest-order modes we calculate eigenfrequencies and eigenfunctions and calculate corresponding intensity and polarization light curves using advanced…
The standard cosmological model does not determine the spatial topology of the universe. This article revisits the signature of a non-trivial topology on the properties of the cosmic microwave background anisotropies. We show that the…
In order to reach the sensitivity required to detect gravitational waves, pulsar timing array experiments need to mitigate as much noise as possible in timing data. A dominant amount of noise is likely due to variations in the dispersion…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
Stochastic temporal wandering of the spin frequency $\nu$ of a rotation-powered pulsar (i.e.~the achromatic component of timing noise unrelated to interstellar propagation) affects the accuracy with which the secular braking torque can be…