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Constructing the field of values of decomposable and general matrices using the ZNN based path following method

numerical LINEAR ALGEBRA WITH APPLICATIONS 2023年第6期30卷 e2513-e2513页

作者： Uhlig, Frank Auburn Univ Dept Math & Stat Auburn AL USA Auburn Univ Dept Math & Stat Auburn AL 36849 USA

This paper describes and develops a fast and accurate path following algorithm that computes the field of values boundary curve partial differential delta F(A) for every conceivable complex or real square matrix A. It relies on the matrix flow decomposition algorithm that finds a proper block-diagonal flow representation for the associated hermitean matrix flow F-A(t)=cos(t)H+sin(t)K under unitary similarity if that is possible. Here F-A(t) is the 1-parameter-varying linear combination of the real and skew part matrices H=(A+A*)/2 and K=(A-A*)/(2i) of A. For indecomposable matrix flows, F-A(t) has just one block and the ZNN based field of values algorithm works with F-A(t) directly. For decomposing flows F-A(t), the algorithm decomposes the given matrix A unitarily into block-diagonal form U*AU=diag(Aj) with j>1 diagonal blocks A(j) whose individual sizes add up to the size of A. It then computes the field of values boundaries separately for each diagonal block A(j) using the path following ZNN eigenvalue method. The convex hull of all sub-fields of values boundary points partial differential F(A(j)) finally determines the field of values boundary curve correctly for decomposing matrices A. The algorithm removes standard restrictions for path following FoV methods that generally cannot deal with decomposing matrices A due to possible eigencurve crossings of FA(t). Tests and numerical comparisons are included. Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and fast when compared with Johnson's Francis QR eigenvalue and Bendixson rectangle based method and compute global eigenanalyses of F-A(tk) for large discrete sets of angles t(k) is an element of[0,2 pi] more slowly.

关键词： block-diagonal matrix decomposable matrix field of values matrix flow numerical algorithm single parameter varying matrices time-varying matrix flow unitary similarity

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Real-time Trajectory Planning for Rail Transit Train Considering Regenerative Energy

Real-time Trajectory Planning for Rail Transit Train Conside...

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IEEE International Conference on Intelligent Transportation Systems

作者： Jianwei Qu Xiaoyun Feng Qingyuan Wang Sch. of Electr. Eng. Southwest Jiaotong Univ. Chengdu China

ISBN: (纸本)9781479960798

This paper proposes an energy efficient driving strategy considering regenerative braking energy, arbitrary speed limits, variable grade profiles and curve radius. In actual operation, the reference speed curve of the Automatic Train Operation (ATO) system needs on-line recalculation when the operation circumstances change, such as delay or a temporary speed limit. An energy-efficient operation optimization model with arbitrary feasible initial and final velocities is built, and the optimal operation modes are obtained by means of the maximum principle. When the braking energy is fully recovered, the speed-holding operation mode is proved to be the most energy-saving regime. Then a numerical algorithm is presented to construct the energy saving speed curve for a given time with the consideration of speed limits. The feasibility of the algorithm is verified through the case study of Shenzhen Metro Line 1. With the flexibility of arbitrary initial and final speed values, the presented algorithm can be applied to ATO system for real-time calculation.

关键词： energy conservation numerical analysis optimisation path planning rapid transit systems regenerative braking ATO system Shenzhen Metro Line 1 arbitrary speed limits automatic train operation braking energy curve radius energy efficient driving strategy energy-efficient operation optimization model energy-saving regime numerical algorithm on-line recalculation optimal operation modes rail transit train real-time trajectory planning regenerative braking energy regenerative energy speed-holding operation mode variable grade profiles Energy efficiency Force Optimization Rail transportation Rails Trajectory

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Discrete State Event-Driven Approach for High-Power Converter Simulations

Discrete State Event-Driven Approach for High-Power Converte...

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IEEE Energy Conversion Congress and Exposition

作者： Bochen Shi Zhengming Zhao Yicheng Zhu Zhujun Yu Jiahe Ju Liqiang Yuan Kainan Chen State Key Laboratory of Control and Simulation of Power System and Generation Equipment Tsinghua University Beijing China

Demands for high-power converters are increasing rapidly. Nevertheless, due to their complex structures and multi-time-scale features, accurate and efficient simulation of such systems has long been a huge obstacle. Aiming at improving the unacceptably slow simulation speed of high-power converters, this paper improves Discrete State Event-Driven (DSED) approach by implementing a decoupling method. Taking a 10kV 1MW electric energy router as an example, this paper evaluates the effectiveness of DSED with the proposed decoupling method in high-power applications. In the studied case, compared with commercially available tool for power electronics simulation, PLECS, DSED can achieve an up to 1000-fold improvement in simulation speed under the same accuracy: PLECS takes 6 hours while DSED only takes 18 seconds. DSED provides a powerful simulation tool for analysis, design and control of high-power converters.

关键词： event-driven simulation numerical algorithm circuit partitioning high-power converter electric energy router solid-state transformer

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Alfvenic-coupling algorithm for global and dynamical magnetosphere-ionosphere coupled system

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JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 2010年第A04期115卷

作者： Yoshikawa, Akimasa Nakata, Hiroyuki Nakamizo, Aoi Uozumi, Teiji Itonaga, Masahiro Fujita, Shigeru Yumoto, Kiyohumi Tanaka, Takashi Kyushu Univ Fac Sci Dept Earth & Planetary Sci Higashi Ku Fukuoka 8128581 Japan Kyushu Univ Space Environm Res Ctr Fukuoka 8128581 Japan Japan Sci & Technol Agcy CREST Kawaguchi Saitama Japan Chiba Univ Grad Sch Sci & Technol Chiba 2638522 Japan Natl Inst Informat & Commun Technol Appl Electromagnet Res Ctr Space Environm Grp Koganei Tokyo 1848795 Japan Yamaguchi Univ Fac Educ Yamaguchi 7538511 Japan Meteorol Coll Kashiwa Chiba 2770852 Japan

This study proposes a new formula that describes a dynamical magnetosphere-ionosphere (MI) coupling system through the field-aligned current (FAC) closure and electrostatic potential connectivity. In the past, MI coupling processes were described as either "inductive'' or "static.'' The inductive coupling scheme is based on the reflection of MHD waves at the ionosphere, whereas in the static coupling scheme the electrostatic potential is determined through the FAC closure. In contrast, in our new formulation these two schemes are combined by the "Alfvenic-coupling'' algorithm. The concept of the Alfvenic coupling is as follows. When a distribution of ionospheric current is changed from the background condition through the mapping of magnetospheric disturbances and/or by the change of ionospheric conductivity, an ionospheric reflection electric filed is instantaneously generated to satisfy the current continuity condition. The electrostatic potential of this reflection field also feeds back to the magnetosphere and excites shear Alfvenic disturbances in the magnetosphere. Therefore, the current continuity condition has to include the FAC of Alfvenic disturbances. In this sense, the reflection potential is not only a modification of the ionospheric potential but also a source of inductive Alfvenic disturbances. Quantitative estimation of feedback components to the magnetosphere reveals that our new formulation is more suitable to global MI simulations than the static MI coupling, which has been the only scheme used in the past.

关键词： MI-coupling global simulation numerical algorithm

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algorithm and software for defining the distribution of eigenvalues of random symmetric matrices via simulation

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2009年第1-11期86卷 1979-1988页

作者： Shmerling, E. Ariel Univ Ctr Samaria Dept Comp Sci & Math IL-44837 Ariel Israel

A simulation algorithm for defining the distribution of eigenvalues of a random symmetric matrix with arbitrary continuous joint probability density function of its entries is presented. The algorithm requires only a uniform random number generator. As a numerical example, the probability that eigenvalues of a certain random symmetric matrix satisfy a given condition is calculated using software implementing the algorithm.

关键词： eigenvalues distribution Monte Carlo simulation random symmetric matrices matlab numerical algorithm

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SIMULTANEOUS POLYNOMIAL APPROXIMATION AND TOTAL VARIATION DENOISING

SIMULTANEOUS POLYNOMIAL APPROXIMATION AND TOTAL VARIATION DE...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Ivan W. Selesnick Polytechnic Institute of New York University Brooklyn NY 11201 USA

ISBN: (纸本)9781479903573

This paper addresses the problem of smoothing data with additive step discontinuities. The problem formulation is based on least square polynomial approximation and total variation denoising. In earlier work, an ADMM algorithm was proposed to minimize a suitably defined sparsity-promoting cost function. In this paper, an algorithm is derived using the majorization-minimization optimization procedure. The new algorithm converges faster and, unlike the ADMM algorithm, has no parameters that need to be set. The proposed algorithm is formulated so as to utilize fast solvers for banded systems for high computational efficiency. This paper also gives optimality conditions so that the optimality of a result produced by the numerical algorithm can be readily validated.

关键词： ADMM optimality of a result produced numerical algorithm Polynomial optimality approximation Problem Formulation Concurrency algorithms Cost functions Polynomial approximation

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Complex Integral Method For Computing Hypersingular Integrals And Error Estimation

Complex Integral Method For Computing Hypersingular Integral...

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The 5th Asia-Pacific International Conference on Computational Methods in Engineering and the 11th Chinese National Conference on Computational Methods in Engineering(ICOME 2015)

作者： Yiming Chen Xuan Li Xuedao Shu Guangxian Shen College of Science Yanshan University Mechanical Engineering and Mechanics Ningbo University College of Mechanical Engineering Yanshan University

In this paper, the complex integral method is firstly put forward to compute hypersingular integrals on interval. Based on the classical Cauchy integral formula, the integral paths of hypersingular integrals is moved to the complex plane from the real axis so that there is no singular points in the new integral paths, and then the computational formulas of the exact value of hypersingular integrals is obtained. At the same time, the numerical algorithm of complex integral and error estimation are derived. numerical examples are provided to show that the method is computationally efficient.

关键词： Hypersingular Integrals Complex Integrals Error Estimation numerical algorithm

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Reaction Control System using Hybrid Micro-Thrusters for Guided Sounding Rocket

Reaction Control System using Hybrid Micro-Thrusters for Gui...

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International Conference on Recent Advances in Space Technologies

作者： Teodor Viorel Chelaru Adrian Chelaru University POLITEHNICA of Bucharest - Research Center for Aeronautics and Space Ghe. Polizu 1 Bucharest Romania INCAS -National Institute for Aerospace Research "Elie Carafoli" B-dul Iuliu Maniu 220 061126 Bucharest Romania

ISBN: (纸本)9781467363952

The paper intend to develop a calculus model for an innovative Reaction Control System (RCS) using hybrid rocket engine technology. Our RCS uses several hybrid micro-thrusters with their thrust modulated by a separate control system. For RCS, each of the thrusters will be able to burn a few minutes and its thrust will be modulated within certain limits by controlling the oxidizer flow. In order to reduce size and weight of the RCS we will use a single oxidizer tank which will have as output a flow distributor. The basic idea is not to stop any of the engines during system's operation but to minimize their thrust reducing the oxidizer flow. This approach is avoiding the inconvenience of repeated stopping and starting of the engine, which can create reliability problems to the entire RCS. By creating thrust imbalance between various hybrid micro thrusters, one can create torques with which the attitude or the trajectory of the vehicle can be adjusted. In terms of calculation model developed, it starts from our theoretical and experimental studies, which aimed to build a computational model for hybrid rocket engine highlighting the scalability, stability and its controllability. These studies were presented in RAST 2011 and are based on our own experiments performed in Electromecanica Ploiesti. Based on this concept we achieve a calculation of the performances of the RCS and an evaluation in their size. Conclusions and any discussion will be focused on technological possibilities for achieving the system and possible areas of application for the RCS.

关键词： hybrid rocket engine nozzle orbital/suborbital vehicle numerical algorithm computation model combustion

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Option pricing with the control variate technique beyond Monte Carlo simulation

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NORTH AMERICAN JOURNAL OF ECONOMICS AND FINANCE 2022年第0期62卷

作者： Chiu, Chun-Yuan Dai, Tian-Shyr Lyuu, Yuh-Dauh Liu, Liang-Chih Chen, Yu-Ting Natl Yang Ming Chiao Tung Univ Inst Informat Management 1001 Daxue Rd Hsinchu 30010 Taiwan Natl Yang Ming Chiao Tung Univ Dept Informat Management & Finance 1001 Daxue Rd Hsinchu 30010 Taiwan Natl Taiwan Univ Dept Comp Sci & Informat Engn Dept Finance 1Sec 4Rooservelt Rd Taipei 10617 Taiwan Natl Taipei Univ Technol Dept Informat & Finance Management 1Sec 3Zhongxiao E Rd Taipei 10634 Taiwan Natl Chengchi Univ Risk & Insurance Res Ctr 64Sec 2ZhiNan Rd Taipei 11605 Taiwan

Although mostly used alongside Monte Carlo simulation, the control-variate (CV) technique can be applied to other numerical algorithms in option pricing. This paper studies the conditions under which a numerical method (simulation-based or not) can benefit from the CV technique and what approximators can serve as CVs. We demonstrate the ideas with Carr and Madan's Fourier transform-based algorithm, convolution-based pricing algorithms, and classic binomial trees. numerical results are provided to show that the CV-enhanced versions are more efficient than the original algorithms.

关键词： numerical algorithm Monte Carlo simulation Control variate Binomial tree Convolution

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Work recognition model for a higher education unit

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COGENT EDUCATION 2023年第2期10卷

作者： Martinez-Vazquez, P. Univ Birmingham Sch Engn Birmingham B15 2TT England

Higher Education frameworks have a strong focus on increasing students' satisfaction. This vision increases expectations on academic performance that often derive from stringent output measures for staff. The combination of internal and external demands for workers, such as those derived from their interaction with society, could create inadequate working conditions, which highlights the need to develop objective, rational, and robust mechanisms to distribute roles and responsibilities more fairly. This paper introduces a work recognition model for managing higher education units. It accounts for individual effort per discretised academic activity over a range of teaching, research, and administration duties. The model integrates standard academic activities into a mathematical framework characterised by continuous derivable functions that can be used to visualise fluctuations of workload across a complete academic year. The established framework enables optimisation of workloads through redistribution, moving away from diagnosing issues experienced by individuals subject to imbalanced or unfair workloads, to propose a practical solution. It is also possible to enhance the architecture of the proposed model to incorporate further activity or allowances and potentially increase robustness. In addition, the numerical model is relatively easy to implement in a variety of platforms. The proposed model was tested on a case study including 26 academics, mixing three-legged and teaching-focused contracts, showing how it decreases the relative differences of workload by a proportion of 4:1, after redistribution.

关键词： project allocation model staff workload numerical algorithm

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