Related papers: An alternative method for solving the Gaussian int…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…
The Gaussian integral, denoted as \( \int_{-\infty}^{\infty} e^{-x^2} dx \), plays a significant role in mathematical literature. In this paper, we explore a family of integrals related to Gaussian functions. Specifically, we introduce…
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the…
In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
A parameter-free method, namely the generalization of the Gauss-Seidel (GGS) method, is developed to solve generalized absolute value equations. Convergence of the proposed method is analyzed. Numerical results are given to demonstrate the…
We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…
Gaussian functions are commonly used in different fields, many real signals can be modeled into such form. Research aiming to obtain a precise fitting result for these functions is very meaningful. This manuscript intends to introduce a new…
q-Gaussian distribution appear in many science areas where we can find systems that could be described within a nonextensive framework. Usually, a way to assert that these systems belongs to nonextensive framework is by means of numerical…
Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path…
In this work, we illustrate and explore the use of Taylor series as solutions of differential equations. For a large a number of classes of differential equations in the literature, there are plenty of sources where the well known Taylor…
The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler--Poisson) integral over a finite boundary, as it is necessary for instance for the error function…
The aim of this paper is to present an efficient numerical procedure to approximate the generalized Abel's integral equations of the first and second kinds. For this reason, the Taylor polynomials and the collocation method are applied.…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…