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Journal of Computational Mathematics 2018年第5期36卷 739-760页

作者： Yunfeng Cai Zhaojun Bai John E. Pask N. Sukumar LMAM & School of Mathematical Sciences Peking University Beijing 100871 China Department of Computer Science and Department of Mathematics University of California Davis CA 95616 USA Physics Division Lawrence Livermore National Laboratory Livermore CA 94550 USA Department of Civil and Environmental Engineering University of California Davis CA 95616 USA

By extending the classical analysis techniques due to Samokish, Faddeev and Faddee- va, and Longsine and McCormick among others, we prove the convergence of the precon- ditioned steepest descent with implicit deflation （PSD-id） method for solving Hermitian- definite generalized eigenvalue problems. Furthermore, we derive a nonasymptotie estimate of the rate of convergence of the PSD-id method. We show that with a proper choice of the shift, the indefinite shift-and-invert preconditioner is a locally accelerated preconditioner, and is asymptotically optimal which leads to superlinear convergence Numerical examples are presented to verify the theoretical results on the convergence behavior of the PSD- id method for solving ill-conditioned Hermitian-definite generalized eigenvalue problems arising from electronic structure calculations. While rigorous and full-scale convergence proofs of preconditioned block steepest descent methods in practical use still largely eludes us, we believe the theoretical results presented in this paper shed light on an improved understanding of the convergence behavior of these block methods.

关键词： Eigenvalue problem steepest descent method Preconditioning Superlinear convergence.

An Enhanced steepest descent method for Global Optimization-Based Mesh Smoothing

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Journal of Applied Mathematics and Physics 2020年第11期8卷 2509-2518页

作者： Kang Zhao Yabang Ma You Wang Xin Yin Yufei Guo Research and Development Centre Sichuan Aerospace Chuannan Initiating Explosive Technology Limited Luzhou China Department of Mechanics and Engineering Science College of Engineering Peking University Beijing China

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

关键词： Mesh Mesh Smoothing Global Mesh Smoothing Optimization-Based steepest descent method

An Enhanced steepest descent method for Global Optimization-Based Mesh Smoothing

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An Enhanced Steepest Descent Method for Global Optimization-...

Soliton resolution and asymptotic stability of N-solutions for the defocusing Kundu–Eckhaus equation with nonzero boundary conditions

作者： Kang Zhao Yabang Ma You Wang Xin Yin Yufei Guo Research and Development Centre Sichuan Aerospace Chuannan Initiating Explosive Technology Limited Department of Mechanics and Engineering Science College of EngineeringPeking University

关键词： Mesh Mesh Smoothing Global Mesh Smoothing Optimization-Based steepest descent method

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Communications in Theoretical Physics 2024年第1期76卷 1-6页

作者： Engui Fan Yanxi Zhang School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Science Fudan UniversityShanghai200433China Tianjin Xinhua High School No.99 machang RoadTianjin300204China

In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS *** the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.

关键词： defocusing Kundu-Eckhaus equation Riemann-Hilbert problems steepest descent method soliton resolution asymptotic stability Painleve transcendents

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Adaptive regularized scheme for remote sensing image fusion

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Frontiers of Earth Science 2016年第2期10卷 236-244页

作者： Sizhang TANG Chaomin SHEN Guixu ZHANG Shanghai Key Laboratory of Multidimensional Information Processing and Department of Computer Science and Technology East China Normal University Shanghai 200241 China Department of Information and Computer Science Shanghai Business School Shanghai 201400 China

We propose an adaptive regularized algorithm for remote sensing image fusion based on variational methods. In the algorithm, we integrate the inputs using a ＂grey world＂ assumption to achieve visual uniformity. We propose a fusion operator that can automatically select the total variation （TV）-LI term for edges and L2-terms for non-edges. To implement our algorithm, we use the steepest descent method to solve the corresponding Euler-Lagrange equation. Experimental results show that the proposed algorithm achieves remarkable results.

关键词： remote sensing image fusion adaptive reg-ulariser variational method steepest descent method

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Rupture model of the 2013 M_W 6.6 Lushan (China) earthquake constrained by a new GPS data set and its effects on potential seismic hazard

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Earthquake Science 2018年第3期31卷 117-125页

作者： Rumeng Guo Yong Zheng Faqi Diao Xiong Xiong Jiao Xu State Key Laboratory of Geodesy and Earth's Dynamics Institute of Geodesy and Geophysics Chinese Academy of Sciences Wuhan 430077 China Institute of Geophysics and Geomatics China University of Geosciences Wuhan 430074 China College of Earth Sciences University of Chinese Academy of Sciences Beijing 100049 China

Vertical records are critically important when determining the rupture model of an earthquake, especially a thrust earthquake. Due to the relatively low fitness level of near-field vertical displacements, the precision of previous rupture models is relatively low, and the seismic hazard evaluated thereafter should be further updated. In this study, we applied three-component displacement records from GPS stations in and around the source region of the 2013 MW6.6 Lushan earthquake to re-investigate the rupture *** improve the resolution of the rupture model, records from both continuous and campaign GPS stations were gathered, and secular deformations of the GPS movements were removed from the records of the campaign stations to ensure their reliability. The rupture model was derived by the steepest descent method（SDM）, which is based on a layered velocity structure. The peak slip value was about 0.75 m, with a seismic moment release of 9.89 × 1018 N·m, which was equivalent to an MW6.6 event. The inferred fault geometry coincided well with the aftershock distribution of the Lushan earthquake. Unlike previous rupture models, a secondary slip asperity existed at a shallow depth and even touched the ground surface. Based on the distribution of the co-seismic ruptures of the Lushan and Wenchuan earthquakes, post-seismic relaxation of the Wenchuan earthquake, and tectonic loading process, we proposed that the seismic hazard is quite high and still needs special attention in the seismic gap between the two earthquakes.

关键词： Lushan earthquake steepest descent method rupture model

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新的松弛非单调线搜索法强收敛性分析

高等学校计算数学学报 2016年第4期38卷 324-329页

作者：胡平淮阴工学院数理学院

1引言无约束最优化问题min{f（x）|x∈R;}有广泛的实际应用背景,很多的学者致力于它的算法研究.其算法一般采用迭代方法求解,在当前迭代点x;处,g;=▽f（xk）≠0,沿搜

关键词： relaxation nonmonotone search algorithm global convergence steepest descent method Unconstrained optimization problem

A Step Tracking on the SOTM

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A Step Tracking on the SOTM

Wave-equation traveltime inversion:Comparison of three numerical optimization methods

2010 3rd IEEE International Conference on Computer Science and Information Technology—ICCSIT 2010

作者： Kunhong Han Wanli Guo Xiquan Gao School of Telecommunication Engineering Xidian University Xi’ an China

In order to solve the problems of slow tracking speed and low accuracy in vehicle mobile satellite communication system, a new step tracking algorithm based on the steepest descent method was proposed. This algorithm adjusted the tracking direction and step size by the steepest descent method, and set the proper threshold to stop tracking. The simulation results showed that the numbers of tracking were reduced to17 steps and tracking accuracy is improved.

关键词： step tracking steepest descent method satellite communication gradient algorithm

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Wave-equation traveltime inversion:Comparison of three numer...