Related papers: Optimal order Jackson type inequality for scaled S…
In this paper, we study the distributed optimization problem using approximate first-order information. We suppose the agent can repeatedly call an inexact first-order oracle of each individual objective function and exchange information…
In this paper, we obtain uniform and non-uniform bounds on the Kolmogorov distance in the normal approximation for Jack deformations of the character ratio, by using Stein's method and zero-bias couplings. Our uniform bound comes very close…
We give stability and consistency results for higher order Gr\"unwald-type formulae used in the approximation of solutions to fractional-in-space partial differential equations. We use a new Carlson-type inequality for periodic Fourier…
We present an algorithm to compute the Jordan chain of a nearly defective matrix with a $2\times2$ Jordan block. The algorithm is based on an inverse-iteration procedure and only needs information about the invariant subspace corresponding…
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…
We consider optimal interpolation of functions analytic in simply connected domains in the complex plane. By choosing a specific structure for the approximant, we show that the resulting first order optimality conditions can be interpreted…
In this paper, we develop a class of samplers for the diffusion model using the operator-splitting technique. The linear drift term and the nonlinear score-driven drift of the probability flow ordinary differential equation are split and…
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect a suitable truncation of the basis expansion of the…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
This paper proposes a novel preconditioned implicit-explicit algorithm enhanced with the extrapolation technique for non-convex optimization problems. The algorithm employs a third-order Adams-Bashforth scheme for the nonlinear and explicit…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is…
We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $l\leq d$ orthogonal directions, where $d$ is the dimension of the ambient space.…
In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious…
Based on the weighted and shifted Gr\"{u}nwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the…
In this paper, we propose numerical scheme for the Riesz space fractional advection-dispersion equations with delay (RFADED). Firstly, analytical solution for RFADED in terms of the functions of Mittag-Leffler type is derived. Secondly, the…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations…
We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $\Phi: \mathbb{R}^d \rightarrow \mathbb{R}$ that is convex and twice…
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…