Related papers: Recursive Harmonic Analysis for Computational of H…
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recursive harmonic numbers, which is like Pascal's triangle, is constructed. A formula for recursive harmonic numbers containing binomial…
This study proposes a recursive and easy-to-implement algorithm to compute the score and Hessian matrix in general regime-switching models. We use simulation to compare the asymptotic variance estimates constructed from the Hessian matrix…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
A method is presented in which matrix elements for some processes are calculated recursively. This recursive calculational technique is based on the method of basis spinors.
We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
A new recursion procedure for deriving renormalized perturbation expansions for the one-dimensional anharmonic oscillator is offered. Based upon the $\hbar$-expansions and suitable quantization conditions, the recursion formulae obtained…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
The usefulness of recursive equations to compute scattering matrix elements for arbitrary processes is discussed. Explicit results at tree and one-loop order, obtained by the HELAC/PHEGAS package that is based on the Dyson-Schwinger…
Harmonic polylogarithms $\H(\vec{a};x)$, a generalization of Nielsen's polylogarithms ${S}_{n,p}(x)$, appear frequently in analytic calculations of radiative corrections in quantum field theory. We present an algorithm for the numerical…
We present a recursive algorithm for multi-coefficient inversion in nonlinear Helmholtz equations with polynomial-type nonlinearities, utilizing the linearized Dirichlet-to-Neumann map as measurement data. To achieve effective recursive…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We study rate of convergence of recursive estimation procedures for the general…
Associated to a finite measure on the real line with finite moments are recurrence coefficients in a three-term formula for orthogonal polynomials with respect to this measure. These recurrence coefficients are frequently inputs to modern…
Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…
We present a method for calculating any (nested) harmonic sum to arbitrary accuracy for all complex values of the argument. The method utilizes the relation between harmonic sums and (derivatives of) Hurwitz zeta functions, which allows a…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…