Related papers: Rational approximation to the Thomas--Fermi equati…
The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace normal approximation in order to give an estimate at the tail…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.
Probably we have observed a new simple phenomena dealing with approximations to two real numbers.
The need for parameter estimation with massive datasets has reinvigorated interest in stochastic optimization and iterative estimation procedures. Stochastic approximations are at the forefront of this recent development as they yield…
Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and…
This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…
Each non-zero point in $\mathbb{R}^d$ identifies a closest point $x$ on the unit sphere $\mathbb{S}^{d-1}$. We are interested in computing an $\epsilon$-approximation $y \in \mathbb{Q}^d$ for $x$, that is exactly on $\mathbb{S}^{d-1}$ and…
We prove almost Strichartz estimates found after adding regularity in the spherical coordinates for Schr\"odinger-like equations. The estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages. Sharpness…
We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Pad\'e approximants that are known to provide the best…
We show that a real rational (over $\C$) surfaces are quasi-simple, i.e., that such a surface is determined up to deformation in the class of real surfaces by the topological type of its real structure.
A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We generalize Dirichlet's diophantine approximation theorem to approximating any real number $\alpha$ by a sum of two rational numbers $\frac{a_1}{q_1} + \frac{a_2}{q_2}$ with denominators $1 \leq q_1, q_2 \leq N$. This turns out to be…
We consider the surface Stokes equation with Lagrange multiplier and approach it numerically. Using a Taylor-Hood surface finite element method, along with an appropriate estimate for the additional Lagrange multiplier, we derive a new…
We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the…
It is an original method based on systems of prameters represented by reals which obey to an infinite descent (convergent sequences). We define calculus of quotients and they conduct quickly to a consequent result. Our own scepticism made…
The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
We propose a framework for model-theoretic stability and simplicity in an approximate first-order setting and generalize some classical results.
We present a rational approximation for the Dawson's integral of real argument and show how it can be implemented for accurate and rapid computation of the Voigt function at small $y < < 1$. The algorithm based on this approach enables…