Related papers: Numerical Approximation of Lambert W Function For …
Mathematical semantic web services are very useful in practice, but only a small number of research results are reported in this area. In this paper we present a method of obtaining an approximation of a mathematical semantic web service,…
In my 2011 Annals of Applied Statistics article [Goerg (2011)] I wrote that "Whereas the Lambert $W$ function plays an important role in mathematics, physics, chemistry, biology and other fields, it has not yet been used in statistics."…
We apply the recently defined Lambert W function to some problems of classical statistical mechanics, i.e. the Tonks gas and a fluid of classical particles interacting via repulsive pair potentials. The latter case is considered both from…
The error function of real argument can be uniformly approximated to a given accuracy by a single closed-form expression for the whole variable range either in terms of addition, multiplication, division, and square root operations only, or…
In this work, the Lambert-Tsallis Wq function is used to provide analytical solutions of fractional polynomials of the type ax^r+bx^s+c = 0. This class of fractional polynomial appears in several areas of physics as well it is in the heart…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for…
The inverse Langevin function is a fundamental part of the statistical chain models used to describe the behavior of polymeric-like materials, appearing also in other fields such as magnetism, molecular dynamics and even biomechanics. In…
We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities…
The paper presents the derivation of the asymptotic behavior of $\nu$-zeros of the modified Bessel function of imaginary order $K_{{\rm i}\nu}(z)$. This derivation is based on the quasiclassical treatment of the exponential potential on the…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with unbroken rays and for…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…
In this work, we establish the response of scalar systems with multiple discrete delays based on the Laplace transform. The time response function is expressed as the sum of infinite series of exponentials acting on eigenvalues inside…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…