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A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as…
In this paper we present a new family of identities for Euler sums and integrals of polylogarithms by using the methods of generating function and integral representations of series. Then we apply it to obtain the closed forms of all…
Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the…
We established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative).…
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated…
The most accurate method to combine measurement from different experiments is to build a combined likelihood function and use it to perform the desired inference. This is not always possible for various reasons, hence approximate methods…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
We study the convergence of a discrete Luenberger observer for the barotropic Euler equations in one dimension, for measurements of the velocity only. We use a mixed finite element method in space and implicit Euler integration in time. We…
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
Parametric and semiparametric tests of circular reflective symmetry about an unknown central direction are developed that are locally and asymptotically optimal in the Le Cam sense against asymmetric $k$-sine-skewed alternatives. The…
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations
Assessing uncertainty is an important step towards ensuring the safety and reliability of machine learning systems. Existing uncertainty estimation techniques may fail when their modeling assumptions are not met, e.g. when the data…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface,…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…