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Let $X$ be lognormal$(\mu,\sigma^2)$ with density $f(x)$, let $\theta>0$ and define ${L}(\theta)=E e^{-\theta X}$. We study properties of the exponentially tilted density (Esscher transform) $f_\theta(x) =e^{-\theta x}f(x)/{L}(\theta)$, in…
Full waveform inversion (FWI) requires an accurate estimation of source signatures. Due to the coupling between the source signatures and the subsurface model, small errors in the former can translate into large errors in the latter. When…
Simple asymptotic expansions for the Jacobi functions $P_\nu^{(\alpha, \beta)}(z)$ and $Q_\nu^{(\alpha, \beta)}(z)$ for large degree $\nu$, with fixed parameters $\alpha$ and $\beta$, are surprisingly rare in the literature, with only a few…
An improved approximation via Havriliak-Negami (HN) functions to the Fourier Transform (FT) of certain Weibull distributions, -\psi_{\beta}, (the time derivative of the Kohlrausch-Williams-Watts function), is given for a large interval of…
A Loewner variational method is developed that allows to calculate arbitrary continuous coefficient functionals of the second, third and fourth coefficients of schlicht functions. Based on this method an improved lower bound for the…
The Burrows-Wheeler transform (BWT) is a well studied text transformation widely used in data compression and text indexing. The BWT of two strings can also provide similarity measures between them, based on the observation that the more…
The Colebrook-White equation is the widely used basis for the calculation of the friction factor lambda for flows in pipes and ducts. Because this equation is implicit in lambda, many solutions have been developed to ease the calculation in…
We propose new weak error bounds and expansion in dimension one for optimal quantization-based cubature formula for different classes of functions, such that piecewise affine functions, Lipschitz convex functions or differentiable function…
The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function \phi(X)---specifically,…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
Fourier series of smooth, non-periodic functions on $[-1,1]$ are known to exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of overcoming these problems is by using a Fourier series on a larger domain, say $[-T,T]$…
This article develops a strengthened convex quadratic convex (QC) relaxation of the AC Optimal Power Flow (AC-OPF) problem and presents an optimization-based bound-tightening (OBBT) algorithm to compute tight, feasible bounds on the voltage…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
In this work we present a simple approximation for the Voigt/comp-lex error function based on fitting with set of the exponential functions of form ${\alpha _n}{\left| t \right|^n}{e^{ - {\beta _n}\left| t \right|}}$, where ${\alpha _n}$…
The Fourier transform truncated on [-c,c] is usually analyzed when acting on L^2(-1/b,1/b) and its right-singular vectors are the prolate spheroidal wave functions. This paper considers the operator acting on the larger space L^2(exp(b|.|))…
We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…
We present an efficient and very flexible numerical fast Fourier-Laplace transform, that extends the logarithmic Fourier transform (LFT) introduced by Haines and Jones [Geophys. J. Int. 92(1):171 (1988)] for functions varying over many…
Laguerre and Laguerre-type polynomials are orthogonal polynomials on the interval $[0,\infty)$ with respect to a weight function of the form $w(x) = x^{\alpha} e^{-Q(x)}, Q(x) = \sum_{k=0}^m q_k x^k, \alpha > -1, q_m > 0$. The classical…
We establish optimal error bounds on an exponential wave integrator (EWI) for the space fractional nonlinear Schr\"{o}dinger equation (SFNLSE) with low regularity potential and/or nonlinearity. For the semi-discretization in time, under the…