Related papers: An iterative method for numerical integration of r…
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of…
We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, the convergence has already been…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
In this study, we explore the integration of Neural Networks, a powerful class of functions known for their exceptional approximation capabilities. Our primary emphasis is on the integration of multi-layer Neural Networks, a challenging…
The aim of this study is to clarify the consequences of recent theoretical results for the numerical computation of expectation by the shift method, and in particular to yield sufficient criteria for the existence of speed of convergence of…
We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
We describe methods to evaluate elementary logarithmic integrals. The integrand is the product of a rational function and a linear polynomial in ln x.
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
The logarithmic model offers new tools for image processing. An efficient method for image enhancement is to use an affine transformation with the logarithmic operations: addition and scalar multiplication. We define some criteria for…
We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definition of one of their iterates drops in degree (over a given…
Landen transformations are maps on the coefficients of an integral that preserve its value. We present a brief survey of their appearnce in the literature.
A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of…
This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series…