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CENTRAL LIMIT THEOREM FOR TEMPORAL AVERAGE OF BACKWARD EULER-MARUYAMA METHOD

Journal of Computational Mathematics 2025年第3期43卷 588-614页

作者： Diancong Jin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific ComputingHuazhong University of Science and TechnologyWuhan 430074China

This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.

关键词： Central limit theorem Temporal average Ergodicity Backward Euler-Maruyama method

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Global Solvability for a Predator-Prey Model with Prey-Taxis and Rotational Flux Terms

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Chinese Annals of Mathematics,Series B 2024年第2期45卷 297-318页

作者： Guoqiang REN Bin LIU School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong Universityof Science and Technology

In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth *** presents the global existence of generalized solutions to the model... 详细信息

关键词： Predator-prey Prey-taxis Giopal existence Kotational flnux

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A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques

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Chinese Annals of Mathematics,Series B 2023年第5期44卷 719-734页

作者： Pengcheng XIE Ya-xiang YUAN State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesUniversity of Chinese Academy of SciencesBeijing 100190China

The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.

关键词： Nonlinear optimization Derivative-Free Quadratic model Line-Search Trust-Region

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Adaptive cyclic gradient methods with interpolation

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Computational Optimization and Applications 2025年 1-25页

作者： Xie, Yixin Sun, Cong Yuan, Ya-Xiang Beijing100876 China Ministry of Education Beijing100876 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way. The Cauchy step is approximated by the quadratic interpolation. And the cycle for stepsize update is adjusted adaptively. Combining with the adaptive nonmonotone line search technique, we prove the global convergence of the proposed method. Furthermore, its sublinear convergence rate for convex problems and R-linear convergence rate for problems with quadratic functional growth property are analyzed. Numerical results show that our proposed algorithm enjoys good performances in terms of both computational cost and obtained function values. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Interpolation

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Stabilization and Blow-up in an Infinite Memory Wave Equation with Logarithmic Nonlinearity and Acoustic Boundary Conditions

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Journal of Systems Science & Complexity 2024年第4期37卷 1368-1391页

作者： PENG Qingqing ZHANG Zhifei School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

In this paper,the authors consider the stabilization and blow up of the wave equation with infinite memory,logarithmic nonlinearity and acoustic boundary *** authors discuss the existence of global solutions for the initial energy less than the depth of the potential well and investigate the energy decay estimates by introducing a Lyapunov ***,the authors establish the finite time blow up results of solutions and give the blow up time with upper bounded initial energy.

关键词： Acoustic boundary condition finite time blow-up general decay infinite memory logarithmic nonlinearity

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Adapted Runge-Kutta Methods for Nonlinear First-Order Delay BVPs with Time-variable Delay

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Acta Mathematicae Applicatae Sinica 2025年第2期41卷 400-413页

作者： Cheng-jian ZHANG Yang WANG Hao HAN School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.

关键词： delay boundary value problems adapted Runge-Kutta method Lagrange interpolation error analysis global stability

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Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 164-191页

作者： Qiang Wen Guo-qiang Ren Bin Liu School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

关键词： diffusive SIS model spontaneous infection periodically evolving domain periodic endemic equilibrium

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On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems

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Applied Numerical Mathematics 2025年 216卷 76-97页

作者： Bai, Zhong-Zhi State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In order to compute the smallest eigenvalue and its corresponding eigenvector of a large-scale, real, and symmetric matrix, we propose a class of greedy randomized coordinate updating iteration methods based on the principle that the indices of larger entries in absolute value of the current residual are selected with a higher probability and, with respect to this index set, the next iterate is updated from the current iterate along with the selected coordinate such that the corresponding entry of the residual is annihilated, resulting in fast convergence rates of the proposed iteration methods. Under appropriate conditions, we prove the convergence of both sequences of the Rayleigh-quotients and the acute angles between the iterates and the eigenvector in terms of the expectation. By numerical experiments, we show that this class of greedy randomized coordinate updating iteration methods are advantageous over the parameterized power method and the coordinate descent method in both iteration counts and computing times. Moreover, with theoretical analysis and computational performance, we confirm that the convergence property of this class of iteration methods can be improved significantly by suitably choosing the arbitrary nonnegative parameter involved in the greedy probability criterion. © 2025 IMACS

关键词： Eigenvalues and eigenfunctions

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SOLVING OPTIMIZATION PROBLEMS OVER THE STIEFEL MANIFOLD BY SMOOTH EXACT PENALTY FUNCTIONS

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Journal of Computational Mathematics 2024年第5期42卷 1246-1276页

作者： Nachuan Xiao Xin Liu The Institute of Operations Research and Analytics National University of SingaporeSingapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of Sciencesand University of Chinese Academy of SciencesChina

In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel *** from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any first-order derivative of the objective *** show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible,namely,are the first-order stationary points of the original optimization problem,or far from the Stiefel ***,the original problem and ExPen share the same second-order stationary ***,the exact gradient and Hessian of ExPen are easy to *** a consequence,abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.

关键词： Orthogonality constraint Stiefel manifold Penalty function

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Multiscale method for identifying and marking the multiform fractures from visible-light rock-mass images

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Underground Space 2024年第3期16卷 279-300页

作者： Yongbo Pan Junzhi Cui Zhenhao Xu School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China The State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China Geotechnical and Structural Engineering Research Center Shandong UniversityJinan 250100China

Multiform fractures have a direct impact on the mechanical performance of rock *** accurately identify multiform fractures,the distribution patterns of grayscale and the differential features of fractures in their neighborhoods are *** on this,a multiscale processing algorithm is *** multiscale process is as *** the neighborhood of pixels,a grayscale continuous function is constructed using bilinear interpolation,the smoothing of the grayscale function is realized by Gaussian local filtering,and the grayscale gradient and Hessian matrix are calculated with high *** small-scale blocks,the pixels are classified by adaptively setting the grayscale threshold to identify potential line segments and *** the global image,potential line segments and mini-fillings are spliced together by progressing the block frontier layer-by-layer to identify and mark multiform *** accuracy of identifying multiform fractures is improved by constructing a grayscale continuous function and adaptively setting the grayscale thresholds on small-scale *** the layer-by-layer splicing algorithm is performed only on the domain of the 2-layer small-scale blocks,reducing the *** using rock mass images with different fracture types as examples,the identification results show that the proposed algorithm can accurately identify the multiform fractures,which lays the foundation for calculating the mechanical parameters of rock masses.

关键词： Visible light rock-mass images Continuous grayscale function Small-scale blocks Multiform fractures

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