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A new type of energy-preserving integrators for quasi-bi-Hamiltonian systems

JOURNAL OF MATHEMATICAL CHEMISTRY 2024年第7期62卷 1667-1681页

作者： Liu, Kai Fu, Ting Shi, Wei Zhou, Xuhuan Nanjing Audit Univ Dept Math Nanjing 211815 Jiangsu Peoples R China Yunnan Normal Univ Yunnan Key Lab Modern Analyt Math & Applicat Kunming 650500 Yunnan Peoples R China Natl Univ Def Technol Dept Math Changsha 410003 Hunan Peoples R China Nanjing Tech Univ Coll Math Sci Nanjing 211816 Jiangsu Peoples R China Nanjing Police Univ Dept Basic Courses Nanjing 210023 Jiangsu Peoples R China

Energy-preserving algorithms, as one of the core research areas in numerical ordinary differential equations, have achieved great success by many methods such as symplectic methods and discrete gradient methods. This paper considers the numerical integration of quasi-bi-Hamiltonian systems, which, as a generalization of bi-Hamiltonian systems, can be expressed in two distinct ways: y=P1(y)del H2(y)=1 rho (y)P2(y)del H1(y). The quasi-bi-Hamiltonian systems have two Hamiltonians H1(y) and H2(y). Conventional discrete gradient methods can only preserve one Hamiltonian at a time. In this paper, based on discrete gradient and projection, new energy-preserving integrators that can preserve the two Hamiltonians simultaneously are proposed. They show better qualitative behaviours than traditional discrete gradient methods do. Numerical integrations of Henon-Heiles type systems and the Korteweg-de Vries (KdV) equation are conducted to show the effectiveness of the new integrators in comparison with traditional discrete gradient methods.

关键词： Quasi-bi-Hamiltonian systems Energy-preserving integrators The discrete gradient methods projection algorithm Henon-Heiles type systems Korteweg-de Vries equation 65L05 65L07 65L20 65P10

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Phase Retrieval with Sparse Phase Constraint

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SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE 2020年第1期2卷 246-263页

作者： Nguyen Hieu Thao Luke, David Russell Soloviev, Oleg Verhaegen, Michel Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands Can Tho Univ Sch Educ Dept Math Can Tho Vietnam Univ Gottingen Inst Numer & Angew Math D-37083 Gottingen Germany Flexible Opt BV NL-2288 GG Rijswijk Netherlands

In this paper, we propose and investigate the phase retrieval problem with the a priori constraint that the phase is sparse (SPR), which encompasses a number of practical applications, for instance, in characterizing phase-only objects such as microlenses, in phase-contrast microscopy, in optical path difference microscopy, and in Fourier ptychography, where the phase object occupies a small portion of the whole field. The considered problem is strictly more general than the sparse signal recovery problem, which assumes the sparsity of the signal because the sparsity of the signal trivially implies the sparsity of the phase, but the converse is not true. As a result, existing solution algorithms in the literature of sparse signal recovery cannot be applied to SPR and there is an appeal for developing new solution methods for it. In this paper, we propose a new regularization scheme which efficiently captures the sparsity constraint of SPR. The idea behind the proposed approach is to perform a metric projection of the current estimated signal onto the set of all the signals whose phase satisfies the sparsity constraint. The main challenge here is that the latter set is not convex and its associated projector in general does not admit a closed form. One novelty of our analysis is to establish an explicit form of that projector when restricted to those points which are relevant to the solutions of SPR. Note that this result is fundamentally different from the widely known calculation form for projections onto intensity constraint sets. Based on this new result, we propose an efficient solution method, named the sparsity regularization on phase (SROP) algorithm, for the SPR problem in the challenging setting where only one point-spread-function image is given, and we analyze its convergence. The algorithm is the combination of the Gerchberg-Saxton (GS) algorithm with the projection step described above. In view of the GS algorithm being equivalent to the alternating pro

关键词： phase retrieval sparsity constraint nonconvex optimization prox-regularity projection algorithm linear convergence

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Model⁃Free Predictive Control for a Kind of High Order Nonlinear Systems

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Journal of Harbin Institute of Technology(New Series) 2022年第2期29卷 62-69页

作者： Ye Tian Baili Su School of Engineering College Qufu Normal UniversityRizhao 276826ShandongChina

For a type of high⁃order discrete⁃time nonlinear systems(HDNS)whose system models are undefined,a model⁃free predictive control(MFPC)algorithm is proposed in this *** first,an estimation model is given by the improved projection algorithm to approach the controlled nonlinear ***,on the basis of the estimation model,a predictive controller is designed by solving the finite time domain rolling optimization quadratic function,and the controller’s explicit analytic solution is also ***,the closed⁃loop system's stability can be ***,the results of simulation reveal that the presented control strategy has a faster convergence speed as well as more stable dynamic property compared with the model⁃free sliding mode control(MFSC).

关键词： nonlinear system compact dynamic linearization(CDL) model predictive control(MPC) model-free control(MFC) projection algorithm

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Narrow-band Interference Suppression Technology of OTH Radar 3

Narrow-band Interference Suppression Technology of OTH Radar

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2002 3rd International Conference on Microwave and Millimeter Wave Technology

作者： YANG Zhi-qun NI Jin-lin LIU Guo-sui Electronic Engineering Research Center of Nanjing University of Science and Technology Nanjing Research Institute of Electronics Technology

ISBN: (纸本)078037486X

In over-the-horizon(OTH) radar,the frequency band is limited to lots of crowded and powerful *** is difficult to find an uncontaminated and broad band,which leads to low range resolution and signal-to-interference and noise ratio(SINR).A desired method is suppressing of interference in a definite *** of the poor sidelobe of pulse compression by notch filtering method,the projection algorithm(PA) and adaptive cancellation algorithm(ACA)are introduced in this *** follows that PA has the advantage of low complexity of computation and low sidelobe by designing sub band filter group,which may introduce temporal ***,ACA can eliminate interference effectively by adjusting the weights although resulting in burden *** further lower sidelobe is obtained which leads to the increase of detection probability greatly.

关键词： range resolution pulse compression sidelobe notch filter projection algorithm adaptive cancellation

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Classification and Applications of Randomized Functional Numerical algorithms for the Solution of Second-Kind Fredholm Integral Equations

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Journal of Mathematical Sciences (United States) 2021年第5期254卷 589-605页

作者： Voytishek, A.V. Institute of Computational Mathematics and Mathematical Geophysics Siberian Branch of the Russian Academy of Sciences Novosibirsk Russian Federation Novosibirsk State University Novosibirsk Russian Federation

Systematization of numerical randomized functional algorithms for approximation of solutions to second-kind Fredholm integral equation is performed in this paper. Three types of algorithms are emphasized: projection algorithms, grid algorithms, and projection-grid algorithms. Disadvantages of grid algorithms that require calculation of values of the kernel of integral equations at fixed points are revealed (practically, the kernels of equation have integrable singularities and this calculation is impossible). Thus, for applied problems related to the solution of second-kind Fredholm integral equations, projection or projection-grid randomized algorithms are more convenient. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： 45B05 65C05 65C40 computational kernel grid algorithm numerical solution projection algorithm randomized algorithm second-kind Fredholm integral equation

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Deployment and configuration of applications for ambient systems 6th

Deployment and configuration of applications for ambient sys...

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6th International Conference on Ambient Systems, Networks and Technologies (ANT) / 5th International Conference on Sustainable Energy Information Technology (SEIT)

作者： Piette, Ferdinand Dinont, Cedric Seghrouchni, Amal El Fallah Taillibert, Patrick Univ Paris 06 Paris France Inst Super Elect & Numer Lille France

Ambient Intelligence (AmI) provides a vision of the information society where heterogeneous hardware entities are disseminated in the environment and used by intelligent agents to provide ubiquitous applications. To ease the integration of new entities in the system, the application and the underlying hardware infrastructure have to be decorrelated. The aim of our research work is to propose mechanisms for the deployment, automatic configuration and monitoring of applications on an heterogeneous hardware infrastructure. In this paper, we model ambient systems to fulfill this purpose. We propose a graph-based mathematical model for ambient systems. This model allows to use a projection algorithm, extending an existing graph matching algorithm, for the deployment and the automatic configuration of applications on an heterogeneous hardware infrastructure. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Ambient Intelligence Graph homomorphism projection algorithm Heterogeneous systems

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Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space

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OPTIMIZATION METHODS & SOFTWARE 2011年第4-5期26卷 827-845页

作者： Censor, Yair Gibali, Aviv Reich, Simeon Univ Haifa Dept Math IL-31905 Haifa Israel Technion Israel Inst Technol Dept Math IL-32000 Haifa Israel

We study two projection algorithms for solving the variational inequality problem in Hilbert space. One algorithm is a modified subgradient extragradient method in which an additional projection onto the intersection of two half-spaces is employed. Another algorithm is based on the shrinking projection method. We establish strong convergence theorems for both algorithms.

关键词： extragradient method Hilbert space projection algorithm subgradient variational inequality

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Subway Rail Fastener Locating Based on Visual Attention Model 13

Subway Rail Fastener Locating Based on Visual Attention Mode...

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13th Asia Pacific Transportation Development Conference - Resilience and Sustainable Transportation Systems

作者： Qi, Wei-Wei Zheng, Shu-Bin Chen, Xing-Jie Li, Li-Ming Shanghai Univ Engn Sci Sch Urban Railway Transportat Shanghai Peoples R China

ISBN: (数字)9780784482902

ISBN: (纸本)9780784482902

Fastener defects detection based on computer vision is an important task in subway rail inspection systems, in which the first step is fastener location. In this paper, a fastener locating method based on visual attention model for subway track is presented, which can implement fastener location in the subway track mixed with ballast-less track in the main line and ballast track on turnout region. Firstly, rail location is obtained by the vertical projection algorithm. Secondly, the image is classified into ballast or ballast-less based on visual attention model with the fractal dimension. Thirdly, ballast image and ballast-less image are treated separately. On one hand, in the ballast image, the sleeper is located with the line segment detector algorithm, and then fastener can be located by the sleeper location combined with the rail location. On the other hand, in the ballast-less image, the fastener is located with horizontal projection algorithm combined with the rail location. Experimental results demonstrate that the proposed method can locate the fastener accurately.

关键词： Fastener Location Visual Attention Model Fractal Dimension projection algorithm Line Segment Detector algorithm

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Parallelization Strategies for Fast Factorized Backprojection SAR on Embedded Multi-Core Architectures

Parallelization Strategies for Fast Factorized Backprojectio...

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IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems (COMCAS)

作者： Wielage, M. Cholewa, F. Riggers, C. Pirsch, P. Blume, H. Leibniz Univ Hannover Inst Microelect Syst D-30167 Hannover Germany

ISBN: (纸本)9781538631690

This paper presents parallelization strategies for the implementation of imaging algorithms for synthetic aperture radar (SAR). Great emphasis is placed on time-domain based algorithms, namely the Global Backprojection algorithm (GBP) and its accelerated version, the Fast Factorized Backprojection algorithm (FFBP). Multi-core platforms are selected for implementation as some combine good performance results with moderate power consumption. The implemented algorithms support several types of parallelization, as the stages of the algorithms can be handled sequentially or interleaved. For the GBP algorithm three different data distribution schemes are investigated. For the FFBP algorithm a successive stage calculation method is compared with a combined calculation method. The performance is exemplary evaluated on the low cost/energy, yet powerful multi-core platform Odroid-XU4. All parallelization strategies show an almost linear speed-up with the number of used cores. Even though a specific multi-core platform is investigated, the design decisions are applicable for general multi-core architectures.

关键词： projection algorithm Radar imaging Parallel algorithms Multicore processing Low-power electronics

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Exponential Stability for Adaptive Control of a Class of First-Order Nonlinear Systems 13th

Exponential Stability for Adaptive Control of a Class of Fir...

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13th International-Federation-of-Automatic-Control (IFAC) Workshop on Adaptive and Learning Control Systems (ALCOS)

作者： Shahab, Mohamad T. Miller, Daniel E. Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

In adaptive control it is typically proven that a weak asymptotic form of stability holds;furthermore, at best it is proven that a bounded noise yields a bounded state. Recently, however, it has been proven in a variety of scenarios that it is possible to carry out adaptive control for a linear-time invariant (LTI) discrete-time plant so that the closed-loop system enjoys exponential stability, a bounded gain on the noise, as well as a convolution bound on the effect of the exogenous inputs;the key idea is to carry out parameter estimation by using the ideal projection algorithm in conjunction with restricting the parameter estimates to a convex set. In this paper we extend the approach to a class of first-order nonlinear systems. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Adaptive Control Nonlinear systems Exponential stability projection algorithm

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