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accurate computation AND INTERPOLATION TECHNIQUE OF FINITE ANALYTIC COEFFICIENTS

Applied Mathematics and Mechanics(English Edition) 1992年第5期13卷 437-444页

作者：张世雄 Institute of Water Conservancy and Hydroelectric Power Research Beijing

The finite analytic method (FA) developed in the last decade is an effective numerical method for solving fluid flow problems. However, because of the limitation in the present computer, large round-off errors are found in calculating FA coefficients when Reynolds number is large. This paper investigates the cause of this difficulty and presents a special programming technique in making an accurate computation of FA coefficients. Then a fundamental function known as 'Pe' is tabulated by the accurate computation. In practical application the interpolation technique is employed so that the FA coefficients can be obtained reliably and quickly.

关键词： finite analytic coefficients high Reynolds number accurate computation interpolation

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Fast and accurate computation of Racah moment invariants for image classification

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PATTERN RECOGNITION 2019年 91卷 100-110页

作者： Benouini, Rachid Batioua, Imad Zenkouar, Khalid Zahi, Azeddine El Fadili, Hakim Qjidaa, Hassan Univ Sidi Mohamed Ben Abdellah Fac Sci & Technol Lab Intelligent Syst & Applicat LSIA BP 2202Route Immouzer Fes 30003 Morocco Univ Sidi Mohamed Ben Abdellah Ecole Natl Sci Appl Fez Fes Morocco Sidi Mohamed Ben Abdellah Univ Fac Sci Dhar El Mehraz LESSI Fes Morocco

In this paper, a new set of moment invariants, named Racah Moment Invariants (RMI), is introduced in the field of image analysis. This new set can be used to describe pattern feature independently of Rotation, Scaling and Translation transforms. Moreover, new fast and accurate algorithm, using recursive method, is developed for accelerating the computation time of the newly proposed invariants, as well as, for enhancing their numerical stability. Subsequently, several experiments have been performed. Initially, the numerical stability and computational cost are depicted. Secondly, the global and local features extraction are clearly illustrated. Then, invariability property and noise robustness are investigated. Finally, the discrimination power and the classification accuracy of the proposed invariants are extensively tested on several publicly available databases. The presented theoretical and experimental results, clearly show that the proposed method can be extremely useful in the fields of image classification. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Racah moment invariants Racah polynomials Fast algorithm accurate computation Direct method Recursive method Image classification Pattern recognition

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Complete and accurate modular numerical computation scheme for multi-coupled electric drive systems

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IET SCIENCE MEASUREMENT & TECHNOLOGY 2020年第3期14卷 259-271页

作者： Nell, Martin Leuning, Nora Moenninghoff, Sebastian Groschup, Benedikt Mueller, Fabian Karthaus, Jan Jaeger, Markus Schroeder, Michael Hameyer, Kay Rhein Westfal TH Aachen IEM Schinkelstr 4 D-52062 Aachen Germany

The accurate computation of multi-coupled electric drive systems is a complex process. In order to consider a variety of physical effects, their interactions as well as the interactions of different components, multiple fields of science have to be addressed. Numerical simulations help to compute these complex systems and to design machines in the best possible way for its specific application. The numerical computation scheme proposed in this study consists of six main sectors: the rough machine design, the preparation of the finite element method including the characterisation and modelling of materials, the electromagnetic simulation, the mechanical simulation, the control and power electronics and the thermal design and simulation. In each of the main sectors, different effects affecting the machine and the system behaviour can be considered and calculated. Depending on the application, they can be added or removed modularly in order to adapt the simulation effort and the simulation accuracy to the application. A detailed insight into the computation methods and approaches in each of these main sectors and their coupling is given in this study.

关键词： electric drives numerical analysis finite element analysis main sectors complete computation scheme accurate modular numerical computation scheme multicoupled electric drive systems accurate computation complex process numerical simulations complex systems rough machine design electromagnetic simulation mechanical simulation thermal design system behaviour simulation effort simulation accuracy computation methods

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Fast computation of accurate Gaussian-Hermite moments for image processing applications

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DIGITAL SIGNAL PROCESSING 2012年第3期22卷 476-485页

作者： Hosny, Khalid M. Zagazig Univ Fac Comp & Informat Dept Informat Technol Zagazig Egypt

Gaussian-Hermite moments are orthogonal moments widely used in image processing and computer vision applications. Similar to the other families of orthogonal moments, highly computational demands represent the main challenging. In this work, an efficient method is proposed for fast computation of highly accurate Gaussian-Hermite moments for gray-level images. The proposed method achieves the accuracy through the integration of Gaussian-Hermite polynomials over the image pixels. To achieve the efficiency, the symmetry property of Gaussian-Hermite polynomials is employed where the computational complexity is reduced by 75%. Fast computational methodology is employed to significantly accelerate the computational process where the 2D Gaussian-Hermite moments are treated in a separated form. Numerical experiments are performed where the results are compared with the conventional method. The comparison of the obtained results clearly ensures the efficiency of the proposed method. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Gaussian-Hermite moments accurate computation Fast algorithm Gray-level images Noise robustness

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Method for verifying solutions of sparse linear systems with general coefficients

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APPLIED MATHEMATICS AND computation 2025年 490卷

作者： Terao, Takeshi Ozaki, Katsuhisa Kyushu Univ Res Inst Informat Technol 744 MotookaNishi Ku Fukuoka Fukuoka 8190395 Japan Shibaura Inst Technol Dept Math Sci 307 FukasakuMinuma Ku Saitama Saitama 3378570 Japan

This paper proposes a verification method for sparse linear systems Ax = b with general and nonsingular coefficient matrices. A verification method produces the error bound for a given approximate solution. Practical methods use one of two approaches. One approach is to verify the computed solution of the normal equation ATAx = AT b by exploiting symmetric and positive definiteness;however, the condition number of ATA is the square of that for A. The other approach applies an approximate inverse of A;however, the approximate inverse of A may be dense even if A is sparse. Additionally, several other methods have been proposed;however, they are considered impractical due to various issues. Here, this paper provides a computing method for verified error bounds using the previous verification method and the latest equilibration. The proposed method can reduce the fill-in and is applicable to many problems. Moreover, we will show the efficiency of an iterative refinement method to obtain accurate solutions.

关键词： Verified numerical computation Sparse linear system Minimum singular value accurate computation

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Analytical solution methods for eigenbuckling of symmetric cross-ply composite laminates

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Chinese Journal of Aeronautics 2017年第1期30卷 282-291页

作者： Xing Yufeng Xiang Wei Institute of Solid Mechanics Beihang University School of Mechanical Engineering Southwest Jiaotong University

Based on the first-order shear deformation theory, this paper explores the analytical methods for eigenbuckling of symmetric cross-ply rectangular composite laminates with a pair of parallel edges simply supported and the remaining two edges arbitrarily constrained. The main contribution of present paper lies in two aspects： one is to present a simple and effective analytical method, namely, the separation-of-variables method, which can generate the closed-form buckling solutions without any computational difficulty; the other is to incorporate the accurate computation method of exponential matrix into the state space technique to avoid the inevitable numerically illconditioned problems reported in several literatures. The results obtained via both analytical methods are identical, and a good agreement with their counterparts in literature is observed. The separation-of-variables method can generate exact solutions within 1 s, which is impossible if the state space method is employed. Besides, the combination of the accurate computation method of exponential matrix and the state space method greatly improves the computational efficiency and gives correct results compared with the straightforward use of state space method.

关键词： accurate computation Analytical solution Composite laminates Eigenbuckling Separation of variablesState space

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A new fast algorithm to compute moment 3D invariants of generalized Laguerre modified by fractional-order for pattern recognition

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MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 2021年第2期32卷 431-464页

作者： El Ogri, O. Karmouni, H. Yamni, M. Daoui, A. Sayyouri, M. Qjidaa, H. Univ Sidi Mohamed Ben Abdellah Fac Sci Dhar El Mahrez Lab Elect Signals & Syst Informat LESSI CED STSTIC Fes Morocco Sidi Mohamed Ben Abdellah Univ Natl Sch Appl Sci Engn Syst & Applicat Lab BP 72My Abdallah AveKm 5Imouzzer Rd Fes Morocco

Orthogonal moments are the projections of image functions on particular functions of the kernel. They play an essential role in image extraction: rotation, scaling, translation invariance, object recognition, image classification, image noise robustness, and low information redundancy. These moments are derived from orthogonal polynomials that can be continuous or discrete. This paper focuses on the fractional-order modified generalized Laguerre moment invariants (FMGLMIs), which is a generalization of the traditional integer order one. In this research, we have developed a new algorithm to compute the 3D invariant moments of FMGLMIs based on the 3D image cuboid representation, our proposed calculation method can improve the efficiency of 3D invariant moment calculation to maintain numerical stability and significantly reduce calculation time with very satisfactory accuracy. To check this new algorithm, the calculation of 3D invariant moments gives very encouraging results for the invariability property of the proposed method with respect to different geometric transformations and noise degradations of 3D images, classification and recognition of 3D images and the calculation time of fractional-order invariants proposed. Finally, the experimental results show that the proposed method makes it possible to construct fractional-order modified generalized Laguerre invariant moments offering better performances for image analysis and pattern recognition.

关键词： Fractional-order modified generalized Laguerre polynomials Fractional-order moment Invariants Fast algorithm accurate computation 3D image classification Pattern recognition

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accurate pseudo Zernike moment invariants for grey-level images

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IMAGING SCIENCE JOURNAL 2012年第4期60卷 234-242页

作者： Hosny, K. M. Zagazig Univ Fac Comp & Informat Dept Informat Technol Zagazig 44519 Sharkia Egypt

Pseudo Zernike moments are orthogonal moments used to represent digital images with minimum amount of information redundancy. Pseudo Zernike moment invariants are image features that are invariant to translation, scaling and rotation which play an essential role in discriminating and classifying similar images where the performance and robustness of the classifiers are highly dependent on the accuracy of these futures. In this work, a new method is presented for accurate computation of two-dimensional pseudo Zernike moment invariants. Approximation errors are removed by using exact geometric and radial geometric moments. Invariance to translation and scaling are computed, while the rotation invariance is directly achieved as direct property of pseudo Zernike moments. Numerical experiments are conducted on a set of standard images. The obtained results demonstrate the efficiency of the proposed method.

关键词： pseudo Zernike moments geometric moments RST accurate computation shape descriptors

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Multi-jet production in hadron collisions

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EUROPEAN PHYSICAL JOURNAL C 2002年第3期24卷 447-458页

作者： Draggiotis, PD Kleiss, RHP Papadopoulos, CG Univ Nijmegen Nijmegen Netherlands NCSR Demokritos Inst Nucl Phys GR-15310 Athens Greece

The advent of high-energy hadron colliders necessitates efficient and accurate computation of multi-jet production processes, both as QCD processes in their own right and as backgrounds for other physics. The algorith... 详细信息

关键词： Production Process Hadron Collider accurate computation Hadron Collision

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Asymptotic behavior of electron densities and computation of one-electron properties

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INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 1996年第6期57卷 1077-1096页

作者： Nunez, MA Departamentos de Matemáticas Física Universidad Autónoma Metropolitana Iztapalapa Apartado Postal 55-534 CP 09340 México Distrito Federal México [*]Departamentos de Matemáticas Física Universidad Autónoma Metropolitana Iztapalapa Apartado Postal 55-534 CP 09340 México Distrito Federal México

The role of the asymptotic behavior of approximating sequences of electron densities rho(n)(r) in the calculation of one-electron properties is studied. Rigorous mathematical results in the frame of Hilbert spaces are used to prove the following facts: (i) Both the L(2) convergence of wave functions psi(n) and the E convergence of the corresponding energies E, guarantee the correctness of the limiting procedure lim(n -->infinity)integral(Omega)s((x) over bar)\psi(n) \(2)d (x) over bar = integral(Omega)s((x) over bar)\psi \(2) d (x) over bar for the most frequently used operators s(x), Omega being any bounded region of the n-particle configuration space R(3N)and (ii) the uniform boundedness of the sequence {p(n)} together with both the L(2) and E convergencies is sufficient to guarantee the correctness of the limiting procedure lim(n -->infinity)integral(0)(infinity) s(r)rho r(2)dr for most one-electron operators s(r) including the power moment operators r(k) which, for large k, are representative of the class of operators not relatively form-bounded by the Hamiltonian. The mathematical concept of uniform boundedness is used to give a characterization of the capability of {rho(n)} to reproduce the asymptotic behavior of the hue electron density rho and it is shown by means of numerical examples how a sequence {p(n)} that does not reproduce the correct asymptotic behavior is not uniformly bounded and can give divergent expectation values of one-electron operators s(r) not relatively form-bounded by the Hamiltonian. (C) 1996 John Wiley & Sons, Inc.

关键词： Rayleigh-ritz method Schrodinger-operators accurate computation Quantum chemistry Convergence Potentials Eigenfunctions Rayleigh-Ritz methods quantum chemistry accuracy class Electron density Eigenfunctions asymptotic behavior asymptotic Converge

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