相关论文: A Robust Approximation to a Lambert-Type Function
Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead…
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…
Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the…
We discuss the best methods available for computing the gamma function $\Gamma(z)$ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small…
We determine the Lagrange function in Taylor polynomial approximation by solving an appropriate initial-value problem. Hence, we determine the remainder term which we then approximate by means of a natural cubic spline. This results in a…
Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights…
We present a new simple algorithm for efficient, and relatively accurate computation of the Faddeyeva function w(z). The algorithm carefully exploits previous approximations by Hui et al [1978] and Humlicek [1982] along with asymptotic…
It is known that the computation of the Voigt/complex error function is problematic for highly accurate and rapid computation at small imaginary argument $y << 1$, where $y = \operatorname{Im} \left[ z \right]$. In this paper we consider an…
GW approximation is one of the most popular parameter-free many-body methods that goes beyond the limitations of the standard density functional theory (DFT) to determine the excitation spectra for moderately correlated materials and in…
The recent progress in the theory of generalized Lambert functions makes possible to solve exactly the Weiss equation of ferromagnetism. However, this solution is quite inconvenient for practical purposes. Precise approximate analytical…
A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument (Y less than 0.1).…
The vivid contrast between two competing algorithms for solving Abel's equation $g(\theta(x)) = g(x) + 1$, given $\theta(x)$, is easily sketched. EJ is faster and more efficient, but ML evaluates a limit characterizing the principal…
In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the…
Using the automatic system GRACE-LOOP, the full $O(\alpha)$ electroweak corrections has been calculated for the process $e^+e^- \to W^+\mu \bar{\nu}_{\mu}$. The total correction to the cross section is found to be typically -6.4% at…
We study the efficiency of the multisection method for univariate nonlinear equations, relative to that for the well-known bisection method. We show that there is a minimal effort algorithm that uses more sections than the bisection method,…
In this paper, we are going to describe the solutions of the functional equation $$ \varphi\Big(\frac{x+y}{2}\Big)(f(x)+f(y))=\varphi(x)f(x)+\varphi(y)f(y) $$ concerning the unknown functions $\varphi$ and $f$ defined on an open interval.…
A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we construct an appropriate constrained free energy functional, such that its…
A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary…
An algorithm for computing eigenvalues and eigenfunctions of the angular spheroidal wave equation, based on a known but scarcely used method, is developed. By requiring the regularity of the wave function, represented by its series…
We establish an explicit formula for the Half-Wave maps equation for rational functions with simple poles. The Lax pair provides a description of the evolution of the poles. By considering a half-spin formulation, we use linear algebra to…