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A double pivot algorithm that combines features of two recently published papers by these authors is proposed. The proposed algorithm is implemented in MATLAB. The MATLAB code is tested, along with a MATLAB implementation of Dantzig's…
We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.
The Wigner rotation matrix ($d$-function), which appears as a part of the angular-momentum-projection operator, plays a crucial role in modern nuclear-structure models. However, it is a long-standing problem that its numerical evaluation…
We introduce a new approach for deterministic sensitivity analysis of Markov reward processes, commonly used in cost-effectiveness analyses, via reformulation into a polynomial system. Our approach leverages cylindrical algebraic…
We prove simple general formulas for expectations of functions of a L\'evy process and its running extremum. Under additional conditions, we derive analytical formulas using the Fourier/Laplace inversion and Wiener-Hopf factorization, and…
Asymmetric Fano line profiles are frequently encountered, e.g., in the photoionization spectra of atoms and ions. For the fitting of spectral line profiles to experimental spectra the line profiles have to be convolved with the experimental…
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…
In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of $O(n^{-1/5})$ for…
This paper introduces a new numerical method for approximating the Lambert W function in the real domain. The method transforms the function into a simpler form that allows iterative refinement of an initial guess. Two iterative strategies…
The Mathieu functions are used to solve analytically some problems in elliptical cylinder coordinates. A computational toolbox was implemented in Matlab. Since the notation and normalization for Mathieu functions vary in the literature, we…
Recently we developed a new sampling methodology based on incomplete cosine expansion of the sinc function and applied it in numerical integration in order to obtain a rational approximation for the complex error function $w\left(z \right)…
The function $y = g(x) = \mathrm{log}\big(W(e^x)\big)$, where $W()$ denotes the Lambert W function, is the solution to the equation $y + e^y = x$. It appears in various problem situations, for instance the calculation of current-voltage…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to…
We seek to develop network algorithms for function computation in sensor networks. Specifically, we want dynamic joint aggregation, routing, and scheduling algorithms that have analytically provable performance benefits due to in-network…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
In this work we show a rational approximation of the Dawson's integral that can be implemented for high-accuracy computation of the complex error function in a rapid algorithm. Specifically, this approach provides accuracy exceeding $\sim…
Routines for computation of Weber's parabolic cylinder functions and their derivatives are implemented in Matlab for both moderate and great values of the argument. Standard, real solutions are considered. Tables of values are included.
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…