相关论文: Evaluation of complex-valued error-like functions …

In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…

We present an efficient multi-accuracy algorithm for the computations of a set of special functions of a complex argument, z=x+iy. These functions include the complex probability function w(z), and closely related functions such as the…

In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative…

The problem of estimating the regression function in a fixed design models with correlated observations is considered. Such observations are obtained from several experimental units, each of them forms a time series. Based on the…

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…

This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…

A randomised trapezoidal quadrature rule is proposed for continuous functions which enjoys less regularity than commonly required. Indeed, we consider functions in some fractional Sobolev space. Various error bounds for this randomised rule…

Dawson's integral and related functions in mathematical physics that include the complex error function (Faddeeva's integral), Fried-Conte (plasma dispersion) function, (Jackson) function, Fresnel function and Gordeyev's integral are…

In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…

An algorithm for the evaluation of the complex exponential function is proposed which is quasi-linear in time and linear in space. This algorithm is based on a modified binary splitting method for the hypergeometric series and a modified…

In neutral meson mixing, a certain class of convolution integrals is required whose solution involves the error function $\mathrm{erf}(z)$ of a complex argument $z$. We show the the general shape of the analytic solution of these integrals,…

In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). When applied to such a problem the classical trapezoidal rule suffers from a loss of accuracy if…

Motivated by the success of Sinkhorn's algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish…

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…

Approximation theory has long been concerned with the development of positive linear operators that effectively approximate classes of functions. Among the most well-known results in this area are Korovkin-type approximation theorems, which…

This paper derives a way to express differentiable complex-valued functions as the sum of powers of $(1-e^{\lambda x})$, where $\lambda\in\mathbb{R}$, with an explicit formula for the remainder. This formulation is then used to associate an…

This paper describes a trapezoidal quadrature method for the discretization of weakly singular, singular and hypersingular boundary integral operators with complex symmetric quadratic forms. Such integral operators naturally arise when…

Integral representations for expectations of functions of a stable L\'evy process $X$ and its supremum $\bar X$ are derived. As examples, cumulative probability distribution functions (cpdf) of $X_T, \barX_T$, the joint cpdf of $X_T$ and…

Consider exponential Carmichael function $\lambda^{(e)}$ such that $\lambda^{(e)}$ is multiplicative and $\lambda^{(e)}(p^a) = \lambda(a)$, where $\lambda$ is usual Carmichael function. We discuss the value of $\sum \lambda^{(e)}(n)$, where…

Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, DCT and IDST, respectively, together with the efficient evaluation of the modified moments by forwards recursions or by…