相关论文: Prony's method and the connected-moments expansion
This paper shows that how to approximate general fuzzy number by using convolution method.
We generalize the notion of an asymptotic weak coupling expansion about an exactly solvable model in quantum mechanics and quantum field theory to an all positive value coupling convergent expansion. This is done by rescaling the variables…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the…
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…
We develop a perturbative approach to study the supersymmetric non-linear sigma model characterized by a generic coupling matrix in the strong coupling limit. The method allows us to calculate explicitly the moments of the eigenfunctions…
In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional…
We introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…
We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having indefinite integral representation. The…
We present a distributed asynchronous algorithm for approximating a single component of the solution to a system of linear equations $Ax = b$, where $A$ is a positive definite real matrix, and $b \in \mathbb{R}^n$. This is equivalent to…
The features of the quasi-static analysis of multiconductor transmission lines by the method of moments are described. Comparison of their efficiency of methods for adaptive mesh refinement is carried out on the example of calculating…
We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains. In this paper, the conjugate function method is extended to cover conformal mappings between Riemannian…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
We continue studying robustness of solving algebraic systems of Prony type (also known as the exponential fitting systems), which appear prominently in many areas of mathematics, in particular modern "sub-Nyquist" sampling theories. We show…