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This work introduces a second-order differential inclusion for unconstrained convex optimization. In continuous level, solution existence in proper sense is obtained and exponential decay of a novel Lyapunov function along with the solution trajectory is derived as well. Then in discrete level, based on numerical discretizations of the continuous differential inclusion, both an inexact accelerated proximal point algorithm and an inexact accelerated proximal gradient method are proposed, and some new convergence rates are established via a discrete Lyapunov function.

We present several fixed point and convergence results for nonexpansive set-valued mappings which map a closed subset of a complete metric space into the space.

We consider the detection of multiple change-points for ρ-mixing sequence. A CUSUM-type method is proposed to estimate the multiple mean change-points and the strong consistency of the multiple mea...

The convergence performance of nonlinear acceleration methods for the method of characteristics (MOC) with flat source (FS) approximation (FS MOC) or linear source (LS) approximation (LS MOC) is nu...

This paper presents a finite difference method for the Rosenau-Kawahara equation, which is performed under pseudo-compactness; this facilitates accuracy improvement. It is shown that the proposed s...

An inertial shadow Douglas-Rachford splitting algorithm for finding zeros of the sum of monotone operators is proposed in Hilbert spaces. Moreover, a three-operator splitting algorithm for solving ...

In this paper we present an application of the Generalized Finite Difference Method to solve the generalized nonlinear Benjamin–Bona–Mahony–Burgers equation in 2D and 3D. We provide two approaches ...

Real life problems are entrenched in ambiguities. To deal with these ambiguities, stochastic functional analysis has emerged as one of the mathematical tools for solving these kinds of problems. Th...

Many real-world problems in applied sciences, engineering and economics can be reformulated as the convex minimization problem of two objective functions. In order to solve this problem, the forwar...

In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex ...

Formulating a control design for integer-valued inputs might be advantageous over, for example, rounding strategies based on a real-valued solution. However, the speed of convergence, computational...

In this paper, to find the numerical solution of the linear systems with the non-Hermitian positive definite matrix, a preconditioned two-sweep shift splitting (PTSS) iteration method is introduced...

Euler [6] and Eisenstein [5] explored the concept of iterated exponents and their convergence. One particular iterated exponent of interest is i(i(i⋰)), which can be shown to converge to z⋆≈0.43828...

In this paper, we consider stochastic differential equations with locally Lipschitz coefficients. Two classes of balanced Euler method are presented. Their moment boundedness and their convergence ...

In this paper, we establish L2-convergence and complete convergence results for the maximum of the partial sum of asymptotically negatively associated random vectors in Hilbert space. In addition, ...

The current paper proposes a new high-order finite difference scheme with low computational complexity to solve the space-time fractional tempered diffusion equation. At the first stage, the time d...

In this paper, we investigate the complete convergence and complete moment convergence of asymptotically almost negatively associated random variables with random coefficients. The obtained results...

In this work, a class of nonstandard finite difference (NSFD) methods is proposed to approximate the exact solution of a diffusive partial differential equation with Burgers convection effect and H...

In this paper, a lower bounded of sequences on classical sampling theorem for random signals is given and is used to extend the applicable range of frame. The convergence property of sampling serie...

To fill the gap in the research on the convergence trend of air pollutants since 2013 in China and overcome the Galton fallacy caused by the parametric regression method, this study examines the convergence trend of the annual average concentration of fine particulate matter 2.5 (PM2.5) in China’s prefecture-level cities after 2013 using a distribution dynamic approach. The winter PM2.5 pollution in Chinese cities is severe. Hence, the convergence of the average winter PM2.5 concentration of prefecturelevel cities is also explored in this study. The results show that during 2015–2019, the annual average PM2.5 concentration level improved significantly. However, the average PM2.5 winter concentration level in 2015–2018 did not significantly decrease, with some cities showing severe pollution levels. The annual average PM2.5 of China’s prefecture-level cities exhibit club convergence, while the PM2.5 concentration in winter exhibits ‘unikurtosis’. In the long run, the annual average PM2.5 clusters around two levels, at approximately 35 lg/m3 and 60 lg/m3 , while the average PM2.5 in winter is concentrated at 100 lg/m3 . In the long run, in the central region, PM2.5 pollution is more severe than in northern and southern areas, regardless of the annual or winter average PM2.5 concentration.

Purpose: To determine the optimal number of data points required for optimization of formulae for classical lens power calculation.\ud \ud Methods: A large dataset of preoperative biometric values was used to assess the convergence of formula constants in a number of established intraocular lens power calculation formulae.\ud \ud Results: In formulae with a single constant, 80 to 100 clinical data points are sufficient to obtain convergence. The Haigis formula (3 constants), requires 200 to 300 data points although refractive error converges more rapidly.\ud \ud Conclusions: In all formulae 80 to 100 clinical data points are sufficient to achieve a stable mean refractive error.

Motivated by computing medians and means, two proximal splitting methods, backward-backward scheme introduced by Passty [Ergodic convergence to a zero of the sum of monotone operators in Hilbert sp...

In general, infill sampling is the core process of efficient global optimization (EGO). Research on infill sampling with few points, high convergence speed and simplicity has received increasing at...

In this paper, based on the properties of slowly varying functions and the de Bruijn conjugates, we establish general results on complete moment convergence for randomly weighted sums of m-asymptot...

A three-level implicit difference scheme is developed for a inviscid Burgers' equation with time delay. It is proved that the proposed scheme is uniquely solvable, stable, and unconditionally conve...

In this correspondence, we investigate mean convergence of order p for the weighted sums of Banach space valued random elements under a suitable (compactly) uniformly integrable condition with or w...

In this paper, the Crank–Nicolson (CN) and rotated four-point Fractional Explicit Decoupled Group (FEDG) methods are introduced to solve the two-dimensional reaction–subdiffusion equation with Capu...

We conjecture a formula supported by computations for the valuation of Kac polynomials of a quiver, which only depends on the number of loops at each vertex. We prove a convergence property of reno...

In this paper, we propose a feasible and effective iteration method for solving the tensor equation A∗NX∗MB=C with a tensor inequality constraint D∗NX∗ME≥F. The global convergence is established. N...

A large number of nonlinear and optimization problems can be reduced to altering point problems. This paper aims to introduce the parallel normal S-iteration technique and study its convergence rat...

A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix ...

The purpose of this article is to study convergence analysis of quasi-variational inequalities using a projection-type method coupled with inertial extrapolation step. First, we give strong converg...

In this paper, we shall discuss the convergence of the continuous-discrete feedback particle filter (FPF) proposed in Yang et al. (2014). The FPF is an interacting system of N particles where the i...

Viscous Burgers' equations with a small viscosity are considered and convergence of vanishing viscosity limit problem is investigated. We examine interior layers of a solution to viscous Burgers' e...

In this paper we establish periodic homogenization for Hamilton-Jacobi-Bellman (HJB) equations, associated to nonlocal operators of integro-differential type. We consider the case when the fractional diffusion has the same order as the drift term, and is weakly elliptic. The outcome of the paper is twofold. One one hand, we provide Lipschitz regularity results for weakly elliptic non-local HJB, extending the results previously obtained in [8]. On the other hand, we establish a convergence result, based on half relaxed limits and a comparison principle for the effective problem. The latter strongly relies on the regularity and the ellipticity properties of the effective Hamiltonian, for which a fine Lipschitz estimate of the corrector plays a crucial role.

The present paper emphasises on equi-statistical convergence, pointwise statistical convergence and uniform statistical convergence for a sequence of real-valued functions by using deferred Cesaro ...

Let the VI indicate a variational inclusion, the CFPP denote a common fixed point problem of countably many nonexpansive mappings, and the SVI represent a system of variational inequalities. We int...

We study the split common fixed point problem with multiple output sets in Hilbert spaces. In order to solve this problem, we propose two new algorithms and establish two strong convergence theorem...

In this paper, we consider Galerkin and multi-Galerkin methods and their iterated versions for solving the nonlinear Hammerstein-type integral equation on the half-line with sufficiently smooth ker...

In this paper, we introduce a new and efficient algorithm for finding a common element of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common ...

Power consumption and data redundancy of wireless sensor networks (WSN) are widely considered for a distributed state monitoring network. For reducing the energy consumption and data amount, we propose a topology optimisation and an iterative parameter identification method for estimating the common model factors in WSN. The former method optimises the decentralised topology such that all the leaf nodes in a community connect to the head node directly. A circle topology is built to enable the remote leaf nodes to link to the head node through two adjoining relay nodes to reduce the whole communication distance and power consumption. Based on the optimised topology, an iterative identification method is proposed to minimise the information capacity by transmitting the processed results instead of raw data to reduce the data amount for calculation and storage. Then, we prove the consensus and convergence of the proposed identification method. Finally, two simulations verify the effectiveness of the proposed method and the comparative results present the data reduction for the on-board calculation, communication, and storage in the practical use of WSN.

In this paper, a new system of variational inclusions involving set-valued quasi-contractive, lower semi-continuous mappings with nonempty closed and convex values is introduced and studied in real...

In this article, we study complete and complete integral convergence theorems for weighted sums of arrays of rowwise widely negative dependent random variables under the sub-linear expectations. Th...

This paper mainly deals with applying a general class of preconditioners to accelerate the convergence speed of some iterative schemes for solving multi-linear systems whose coefficient tensors are...

In this paper, an efficient finite difference scheme is proposed for one dimension and two dimension coupled space fractional nonlinear Schrodinger equations. First, the high-order difference schem...

In this paper. we consider fuzzy Volterra integral equation of the second kind with weakly singular kernel. We prove existence and uniqueness of the solution. When analyzing the convergence of a nu...