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Isochronicity Problem of Higher-Order Singular Point for Polynomial Differential Systems

ACTA APPLICANDAE MATHEMATICAE 2010年第3期110卷 1429-1448页

作者： Wu, Yusen Zhang, Cui Li, Peiluan Cent S Univ Sch Math Sci & Comp Technol Changsha 410075 Hunan Peoples R China Luoyang Normal Univ Sch Math Sci Luoyang 471022 Henan Peoples R China

Due to the difficulty, the isochronicity problems with respect to higher-order singular point (or degenerate singular point) of polynomial differential systems are far from being solved. The calculation of period constants is an effective way to find necessary conditions for isochronicity. In this paper, by means of a homeomorphic transformation, higher-order singular point is transferred into the origin. At the same time, a new recursive algorithm to compute period constants at the origin of the transformed system is deduced which is easy to realize with the computer algebraic system such as MATHEMATICA or MAPLE. Finally, to illustrate the effectiveness of our algorithm, the pseudo-isochronous center conditions of higher-order singular point for a class of septic system are investigated. Our work is new in terms of research about the isochronicity problem of higher-order singular point and consists of the existing results related to the origin as a special case when it is an elementary singular point.

关键词： Higher-order singular point Period constant recursive algorithm Polynomial differential system

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APPROXIMATION OF A LINEAR DYNAMIC PROCESS MODEL USING THE FREQUENCY APPROACH AND A NON-QUADRATIC MEASURE OF THE MODEL ERROR

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INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE 2014年第1期24卷 99-109页

作者： Janiszowski, Krzysztof B. Warsaw Univ Technol Inst Automat Control & Robot PL-02525 Warsaw Poland

The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e. g., determined as a result of discrete-time identification. The approximation is derived for minimization of a non-quadratic performance index. This index can be determined as an exponent or absolute norm of an error. Two algorithms for determination of the approximation coefficients are considered, a batch processing one and a recursive scheme, based on the well-known on-line identification algorithm. The proposed approach is not sensitive to local outliers present in the original frequency response. Application of the approach and its features are presented on examples of two simple dynamic systems.

关键词： approximation method frequency domain non-quadratic criterion recursive algorithm

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recursive Identification of Continuous Two-Dimensional Systems in the Presence of Additive Colored Noise

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IETE JOURNAL OF RESEARCH 2014年第1期60卷 74-84页

作者： Shafieirad, Mohsen Shafiee, Masoud Abedi, Mehrdad Amirkabir Univ Technol Dept Elect Engn Tehran Iran Amirkabir Univ Technol SIC Res Inst Tehran Iran

In this paper, a recursive algorithm is developed to estimate the parameters of a partial differential equation as a continuous two-dimensional (2-D) system in the presence of additive colored noise. The system is modelled as hybrid Box-Jenkins model. No comprehensive algorithm for identification of continuous 2-D systems simultaneous with noise process parameter estimation has been proposed so far. Also, there is no recursive method to identify the continuous 2-D systems. The proposed algorithm estimates the noise-free system parameters and colored noise process parameters based on the instrumental variable method simultaneously. Finally, the performance of the proposed method is evaluated by a numerical example.

关键词： Two-dimensional continuous systems recursive algorithm Instrumental variable Stochastic estimation

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A fast algorithm for multilevel thresholding

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JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 2001年第5期17卷 713-727页

作者： Liao, PS Chew, TS Chung, PC ChengShiu Inst Technol Dept Elect Engn Kaohsiung 833 Taiwan Natl Cheng Kung Univ Dept Engn Sci Tainan 701 Taiwan Natl Cheng Kung Univ Dept Elect Engn Tainan 701 Taiwan

Otsu reference proposed a criterion for maximizing the between-class variance of pixel intensity to perform picture thresholding. However, Otsu's method for image segmentation is very time-consuming because of the inefficient formulation of the between-class variance. In this paper, a faster version of Otsu's method is proposed for improving the efficiency of computation for the optimal thresholds of an image. First, a criterion for maximizing a modified between-class variance that is equivalent to the criterion of maximizing the usual between-class variance is proposed for image segmentation. Next, in accordance with the new criterion, a recursive algorithm is designed to efficiently find the optimal threshold. This procedure yields the same set of thresholds as the original method. In addition, the modified between-class variance can be pre-computed and stored in a look-up table. Our analysis of the new criterion clearly shows that it takes less computation to compute both the cumulative probability (zeroth order moment) and the mean (first order moment) of a class, and that determining the modified between-class variance by accessing a look-up table is quicker than that by performing mathematical arithmetic operations. For example, the experimental results of a five-level threshold selection show that our proposed method can reduce down the processing time from more than one hour by the conventional Otsu's method to less than 107 seconds.

关键词： Otsu's thresholding image segmentation picture thresholding multilevel thresholding recursive algorithm

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ONLINE PARAMETER ESTIMATION USING MATRIX PSEUDOINVERSE

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PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1971年第8期118卷 1041-+页

作者： SINHA, NK PILLE, W Department of Electrical Engineering Defence Research Establishment Valcartier Courcelette Canada Department of Electrical Engineering McMaster University Hamilton Canada

A method based on the matrix pseudoinverse is presented for the online identification of discrete-time systems of known order. recursive algorithms are described which provide minimum-norm estimates of the parameter vector when insufficient data are available, and least-squares estimates with adequate data. These estimates can be updated easily with each pair of additional input-output data, as matrix inversion is not required. When the order of the system is not known, it may be determined offline using one of the two methods described. A recursive algorithm for calculating the residual error is also derived. A number of examples are given to illustrate the usefulness of the methods.

关键词： a priori probability density residual error mathematical model input output data contaminating noise identification parameter vector discrete time systems recursive algorithm online identification matrix algebra statistics least square estimates matrix pseudoinverse physical plant Simulation, modelling and identification online operation matrix inversion noise Discrete control systems minimum norm estimates

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Function-valued Pade-type approximant via E-algorithm and its applications in solving integral equations

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APPLIED MATHEMATICS AND COMPUTATION 2011年第20期217卷 7975-7984页

作者： Gu, Chuanqing Tao, Youtian Shanghai Univ Dept Math Shanghai 200444 Peoples R China Chaohu Coll Dept Math Chaohu 238000 Peoples R China

The function-valued Pade-type approximant (FPTA) was defined in the inner product space [8]. In this work, we choose the coefficients in the Neumann power series to make the inner product with both sides a function-valued system of equations to yield a scalar system. Then we express an FPTA in the determinant form. To avoid the direct computation of the determinants, we present the E-algorithm for FPTA based on the vector-valued E-algorithm given by Brezinski [4]. The method of FPTA via E-algorithm (FPTAVEA) not only includes all previous methods but overcomes their essential difficulties. The numerical experiment for a typical integral equation [1] illustrates that the method of FPTAVEA is simpler and more effective for obtaining the characteristic values and the characteristic functions than all previous methods. In addition, this method is also applicable to other Fredholm integral equations of the second kind without explicit characteristic values and characteristic functions. A corresponding example [12] is given and the numerical result is the same as that in [12]. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Function-valued pade approximant Fredholm integral equation recursive algorithm Characteristic value Characteristic function

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A new bivariate basis representation for Bezier-based triangular patches with quadratic complexity

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2011年第8期61卷 2292-2295页

作者： Dejdumrong, Natasha King Mongkuts Univ Technol Thonburi Fac Engn Dept Comp Engn Bangkok 10140 Thailand

A new class of bivariate bases for the triangular surface construction, based on quadratic and cubic bivariate Bernstein polynomials, is proposed, by extending a model for the univariate basis with linear complexity. This new basis is recursively expressed by its recurrence formulae which are provided, and its important geometric properties are also described. In addition, a recursive algorithm for calculating a point on this triangular surface is recursively defined in the same manner as in the well known de Casteljau algorithm. The main advantage of this model is its recursive algorithm that is proven to construct a triangular surface of degree n in quadratic computational complexity, O(n(2)). (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Bezier triangular patches Recurrence formulae recursive algorithm Quadratic complexity

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Space curve fitting method based on fiber-optic curvature gages

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OPTICS AND LASER TECHNOLOGY 2012年第1期44卷 290-294页

作者： Di, Haiting NE Forestry Univ Coll Engn & Technol Harbin 150040 Peoples R China

A novel fiber-optic curvature gage, which can measure curvature directly, has been developed in recent years. In order to measure the bending and torsional deformation of space curve shape, an array of looped fiber-optic curvature gages are arranged on two symmetrical surfaces of a flexible layer to form a gage layer system. A calibration method of the gage layer system is proposed. Based on the bending curvature and twist values of space curve structure provided by gage layer system, a moving coordinate system is established by curve tangent and curvature vectors through a differential geometry method. The osculating plane is determined by twist angle in the moving coordinate system. The calculation of curve bending and analysis of the moving coordinate system transformation can be carried out in osculating plane. Then, the space curve is divided into many easily analyzed plane curves. recursive algorithm is used to obtain the position information of space curve points and the space curve fitting can be realized. The correlative formulas are deduced and the algorithm is validated by a simulation example. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Space curve fitting Fiber-optic curvature gage recursive algorithm

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Analysis of interconnects with frequency-dependent parameters by differential quadrature method

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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS 2005年第12期15卷 877-879页

作者： Tang, M Mao, JF Li, XC Jiao Tong Univ Dept Elect Engn Shanghai 200030 Peoples R China

This letter presents an efficient numerical method for the transient analysis of interconnects with frequency-dependent parameters. The development of interconnects model starts from frequency-domain Telegrapher's equations, and the time-domain equations including convolutions are obtained by inverse Laplace transform. Then, the differential quadrature method (DQM) approximates them to a set of ordinary differential equations. The numerical convolution items are calculated by recursive algorithm, which leads to high efficiency of this method. In addition, the model does not use any restrictive assumptions on the frequency dependence of interconnects parameters. A numerical example is presented to demonstrate the accuracy and efficiency of the proposed method.

关键词： differential quadrature method (DQM) frequency-dependent parameters interconnects recursive algorithm

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Novel algorithm for continuous decoding of turbo codes

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IEE PROCEEDINGS-COMMUNICATIONS 1999年第5期146卷 271-274页

作者： Bai, B Ma, X Wang, X Xidian Univ Natl Key Lab Integrated Serv Network Xian 710071 Peoples R China

A novel type of recursive algorithm for decoding turbo codes with a convolutional interleaver is proposed, based on a symbol-by-symbol maximum a posteriori probability algorithm. It requires only a forward recursion which can be performed in parallel, and the number of variables to be stored does not increase with decoding delay. This algorithm can be used in continuous decoding for both recursive and nonrecursive encoders. Simulation results of demonstrating its performance are presented.

关键词： recursive encoders forward recursion continuous decoding turbo codes nonrecursive encoders soft-output algorithm Codes error correction codes interleaved codes MAP algorithm symbol-by-symbol maximum a posteriori probability algorithm convolutional codes convolutional interleaver decoding recursive algorithm

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