Related papers: Numerical Methods for the Inverse Nonlinear Fourie…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this…
First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. The problem of finding or computing first passage distributions is, in general, quite challenging. We…
A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules is introduced.
This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional…
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
This paper is presented to give numerical solutions of some cases of nonlinear wave-like equations with variable coefficients by using Reduced Differential Transform Method (RDTM). RDTM can be applied most of the physical, engineering,…
The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are…
We propose an alternative approach that avoids the nonlinear equations for the Fourier coefficients that appear in the method of harmonic balance. We apply it to two simple illustrative examples.
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper…
This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only $17$ summation terms the…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save…
Based on the definition of the Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the fractional Fourier transform, we have obtained the discrete fractional Fourier…
The problem of applying Nash-Moser Newton methods to obtain periodic solutions of the compressible Euler equations has led authors to identify the main obstacle, namely, how to invert operators which impose periodicity when they are based…
We survey and investigate some computational aspects of the Fourier-Mukai transform.
The nonuniform discrete Fourier transform (NUDFT) and its inverse are widely used in various fields of scientific computing. In this article, we propose a novel superfast direct inversion method for type-III NUDFT. The proposed method…