Related papers: Computing the Lambert W function in arbitrary-prec…
We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…
Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a…
We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical…
Complex interval arithmetic is a powerful tool for the analysis of computational errors. The naturally arising rectangular, polar, and circular (together called primitive) interval types are not closed under simple arithmetic operations,…
Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is…
The paper contains the proof of $L^p$-weighted norm inequalities for both, martingales square functions and the classical square functions in harmonic analysis of Littlewood-Paley and Lusin. Furthermore, the bounds are completely explicit…
We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…
In this paper, we describe a comprehensive algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) using a generalized branch-and-cut approach. The framework presented merges features from existing…
In this tutorial survey we recall the basic properties of the special function of the Mittag-Leffler and Wright type that are known to be relevant in processes dealt with the fractional calculus. We outline the major applications of these…
Walley's Imprecise Dirichlet Model (IDM) for categorical data overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the…
An algorithm for computing the nonlinearity of a Boolean function from its algebraic normal form (ANF) is proposed. By generalizing the expression of the weight of a Boolean function in terms of its ANF coefficients, a formulation of the…
We prove sharp $L^p(w)$ norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the $A_p$ characteristic of $w$ for all $1<p<\infty$. This implies the same sharp inequalities for the classical…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
We prove $l^p$-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of $p$ in all dimensions $n\ge 2$.
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex…
Walley's Imprecise Dirichlet Model (IDM) for categorical i.i.d. data extends the classical Dirichlet model to a set of priors. It overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in…