Related papers: High-precision numerical evaluation of Lauricella …
A numerical scheme is developed for the evaluation of Abramowitz functions $J_n$ in the right half of the complex plane. For $n=-1,\, \ldots,\, 2$, the scheme utilizes series expansions for $|z|<1$ and asymptotic expansions for $|z|>R$ with…
Using the theory of functions of several variables and $q$-calculus, we prove an expansion theorem for the analytic function in several variables which satisfies a system of $q$-partial differential equations. Some curious applications of…
We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…
We propose a novel method for reconstructing Laurent expansion of rational functions using $p$-adic numbers. By evaluating the rational functions in $p$-adic fields rather than finite fields, it is possible to probe the expansion…
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic…
In this paper, we derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function in several variables. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
The aim of this paper is to give linear independence results for the values of certain series. As an application, we derive arithmetical properties of the sums of reciprocals of Fibonacci and Lucas numbers associated with certain coprime…
In this paper, we study the solutions of the system of bilateral type matrix differential equations and presented these solutions in terms of Lauricella hypergeometric matrix functions of several variables and Srivastava's triple…
Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high-dimensional…
We introduce inferential methods for prediction based on functional random effects in generalized functional mixed effects models. This is similar to the inference for random effects in generalized linear mixed effects models (GLMMs), but…
A new highly accurate algorithm for the solution of the Falkner-Skan equation of boundary layer theory is presented. The algorithm, based on a Maclaurin series representation, finds its coefficients from recurrence. In addition,…
Parameter estimation in HEP experiments often involves Monte-Carlo simulation to model the experimental response function. A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization…
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…
The focus of this work is a posteriori error estimation for stochastic Galerkin approximations of parameter-dependent linear elasticity equations. The starting point is a three-field PDE model in which the Young's modulus is an affine…
Recursive algorithms for computing the Frobenius norm of a real array are proposed, based on hypot, a hypotenuse function. Comparing their relative accuracy bounds with those of the BLAS routine DNRM2 it is shown that the proposed…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of…