Related papers: Multiple-location matched approximation for Bessel…

In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance…

We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link…

It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for…

A useful semiclassical method to calculate eigenfunctions of the Schroedinger equation is the mapping to a well-known ordinary differential equation, as for example Airy's equation. In this paper we generalize the mapping procedure to the…

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this…

For metric spaces with curvature less than or equal to x, x<0, it is shown that a recurrent geodesic can be approximated by closed geodesics. A counter example is provided for the converse.

Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…

Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that…

In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinatorial, while most existing approaches are based on algebra…

We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…

We present in this work alternative analytic formulations for the fan-beam tomographic backprojection operation and its associated adjoint transform in standard (equiangular) and linear (equidistant) detector geometries. The proposed…

We present a new semiclassical method that yields an approximation to the quantum mechanical wavefunction at a fixed, predetermined position. In the approach, a hierarchy of ODEs are solved along a trajectory with zero velocity. The new…

This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…

Motivated by the mathematics literature on the algebraic properties of so-called polynomial vector flows, we propose a technique for approximating nonlinear differential equations by linear differential equations. Although the idea of…

The derivatives with respect to order {\nu} for the Bessel functions of argument x (real or complex) are studied. Representations are derived in terms of integrals that involve the products pairs of Bessel functions, and in turn series…

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many…

We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…