Related papers: Recursive Harmonic Analysis for Computational of H…
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection…
A three term recurrence relation is derived for a basis consisting of polynomials multiplied by sines and cosines with large, but fixed frequencies. A numerical method for computing the coefficients of the three term recurrence relation is…
Discrete Hahn polynomials (DHPs) and their moments are considered to be one of the efficient orthogonal moments and they are applied in various scientific areas such as image processing and feature extraction. Commonly, DHPs are used as…
A generalization of a recently introduced recursive numerical method for the exact evaluation of integrals of regular solid harmonics and their normal derivatives over simplex elements in $\mathbb{R}^3$ is presented. The original Quadrature…
We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper conditional regularity results when compared…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synthetic data sets with 50--500 data points and dimensionality…
Fast, accurate, and stable computation of the Clebsch-Gordan (C-G) coefficients is always desirable, for example, in light scattering simulations, the translation of the multipole fields, quantum physics and chemistry. Current recursive…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation…
We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We…
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…
Combinig the harmonic balance method (HBM) and a continuation method is a well-known technique to follow the periodic solutions of dynamical systems when a control parameter is varied. However, since deriving the algebraic system containing…
A recursive approach for shrinking coefficients of an atomic decomposition is proposed. The corresponding algorithm evolves so as to provide at each iteration a) the orthogonal projection of a signal onto a reduced subspace and b) the index…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We present an efficient method for the computation of homogenized coefficients of divergence-form operators with random coefficients. The approach is based on a multiscale representation of the homogenized coefficients. We then implement…