相关论文: Rates of convergence for iterative solutions of eq…

In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…

We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…

This article aims to present the $AT$ algorithm, a novel two-step iterative approach for approximating fixed points of weak contractions within complete normed linear spaces. The article demonstrates the convergence of $AT$ algorithm…

We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We prove some…

In the iterative algorithm recently proposed by Waxman for solving eigenvalue problems, we point out that the convergence rate may be improved. For many non-singular symmetric potentials which vanish asymptotically, a simple analytical…

In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…

This paper introduces a general framework for iterative optimization algorithms and establishes under general assumptions that their convergence is asymptotically geometric. We also prove that under appropriate assumptions, the rate of…

We give almost sure convergence rate bounds of ratio consensus algorithms when the protocol can be reformulated to be linear updates of vector values on a possibly larger, augmented network. This is an improvement of the results of…

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…

We prove convergence with optimal algebraic rates for an adaptive finite element method for nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also includes the iterative and inexact solution of the…

We show that only a rather small proportion of linear equations are solvable in elements of a fixed finitely generated subgroup of a multiplicative group of a number field. The argument is based on modular techniques combined with a…

We give some Korovkin-type theorems on convergence and estimates of rates of approximations of nets of functions, satisfying suitable axioms, whose particular cases are filter/ideal convergence, almost convergence and triangular…

In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…

Methods of deep learning have become increasingly popular in recent years, but they have not arrived in compositional data analysis. Imputation methods for compositional data are typically applied on additive, centered or isometric…

In this paper, we study the nonexpansive properties of metric resolvent, and present a convergence rate analysis for the associated fixed-point iterations (Banach-Picard and Krasnosel'skii-Mann types). Equipped with a variable metric, we…

Iterative hard thresholding (IHT) has gained in popularity over the past decades in large-scale optimization. However, convergence properties of this method have only been explored recently in non-convex settings. In matrix completion,…

In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general…

This paper proposes uni-orthogonal and bi-orthogonal nonnegative matrix factorization algorithms with robust convergence proofs. We design the algorithms based on the work of Lee and Seung [1], and derive the converged versions by utilizing…

In this paper we apply methods of proof mining to obtain a highly uniform effective rate of asymptotic regularity for the Ishikawa iteration associated to nonexpansive self-mappings of convex subsets of a class of uniformly convex geodesic…

The optimization problems associated with training generative adversarial neural networks can be largely reduced to certain {\em non-monotone} variational inequality problems (VIPs), whereas existing convergence results are mostly based on…