相关论文: Approximating 1 from below using $n$ Egyptian frac…

We survey the classical results of the Dirichlet Approximation Theorem.

In this document, as far as the authors know, an approximation to the zeros of the Riemann zeta function has been obtained for the first time using only derivatives of constant functions, which was possible only because a fractional…

We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…

Let $f: {\Bbb R}^n \longrightarrow {\Bbb R}$ be a positive definite quadratic form and let $y \in {\Bbb R}^n$ be a point. We present a fully polynomial randomized approximation scheme (FPRAS) for computing $\sum_{x \in {\Bbb Z}^n}…

This note summarizes the steps to computing the best-fitting affine reflection that aligns two sets of corresponding points.

We call positive integer n a near-perfect number, if it is sum of all its proper divisors, except of one of them ("redundant divisor"). We prove an Euclid-like theorem for near-perfect numbers and obtain some other results for them.

We develop a method for calculating Riemann sums using Fourier analysis.

We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational…

A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…

We factor the number 157573 using an NMR implementation of Gauss sums.

A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…

In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.

In this didactic note, we describe a procedure to derive successive approximations of $\pi$ using Euler Beta functions. It is an interesting exercise for undergraduate students, since it involves polynomial roots, integral calculations,…

ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi- Monte Carlo) sequences. We show that the resulting ABC…

Let $F_{n}$ be the $n$-th Fibonacci number. Put $\varphi=\frac{1+\sqrt5}{2}$. We prove that the following inequalities hold for any real $\alpha$: 1) $\inf_{n \in \mathbb N} ||F_n\alpha||\le\frac{\varphi-1}{\varphi+2}$, 2) $\liminf_{n\to…

We give the q-analogue of the sums of the n-th powers of positive integers up to k-1.

In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the…

In this paper we study the subset sum problem with real numbers. Starting from the given problem, we formulate a quadratic maximization problem over a polytope which is eventually written as a distance maximization to a fixed point. For…

We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational…

Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which…