Related papers: $\alpha$-Parameterized Differential Transform Meth…
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…
The method of characteristics has played a very important role in mathematical physics. Preciously, it was used to solve the initial value problem for partial differential equations of first order. In this paper, we propose a fractional…
In this paper, we introduce a novel approach called the Iterative Aboodh Transform Method (IATM) which utilizes Daftardar--Jafari polynomials for solving non-linear problems. Such method is employed to derive solutions for non-linear…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…
We give two algebro-geometric inspired approaches to fast algorithms for Fourier transforms in algebraic signal processing theory based on polynomial algebras in several variables. One is based on module induction and one is based on a…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
In contrast to previous analyses, we demonstrate a Bayesian approach to the estimation of the CKM phase $\alpha$ that is invariant to parameterization. We also show that in addition to {\em computing} the marginal posterior in a Bayesian…
Kunchenko's method of polynomial maximization provides a semiparametric apparatus for parameter estimation under non-Gaussian errors, but its classical power basis relies on finite higher-order integer moments. This paper introduces the…
Transformer-based methods have achieved remarkable results in image super-resolution tasks because they can capture non-local dependencies in low-quality input images. However, this feature-intensive modeling approach is computationally…
Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified implements…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
This paper shows that it is possible to improve the computational cost, the memory requirements and the accuracy of Quick Fourier Transform (QFT) algorithm for power-of-two FFT (Fast Fourier Transform) just introducing a slight modification…
We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor's formula monomial basis. Error bounds for the…
We introduce a truncated $M$-fractional derivative type for $\alpha$-differentiable functions that generalizes four other fractional derivatives types recently introduced by Khalil et al., Katugampola and Sousa et al., the so-called…
Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…
A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical method is an elegant combination of the Natural Transform Method (NTM) and a well-known method,…