Search results for: local linear approximation method.

Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: Approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median.

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Authors: Ranjan Kumar Dash, Chita Ranjan Tripathy

Abstract:

The evaluation of residual reliability of large sized parallel computer interconnection systems is not practicable with the existing methods. Under such conditions, one must go for approximation techniques which provide the upper bound and lower bound on this reliability. In this context, a new approximation method for providing bounds on residual reliability is proposed here. The proposed method is well supported by two algorithms for simulation purpose. The bounds on residual reliability of three different categories of interconnection topologies are efficiently found by using the proposed method

Keywords: Parallel computer network, reliability, probabilisticgraph, interconnection networks.

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Authors: Peng Li, Chuanri Li, Tao Li

Abstract:

Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method, and gives concrete processes on determining the factor and sub-factor sets, weight sets, judgment set, and multi-stage fuzzy evaluation. To determine the weight of factor and sub-factor sets, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: Reliability allocation, fuzzy arithmetic, allocation weight.

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Authors: O. H. Colak, T. C. Destici, S. Ozen, H. Arman, O. Cerezci

Abstract:

The wavelet transform is one of the most important method used in signal processing. In this study, we have introduced frequency-energy characteristics of local earthquakes using discrete wavelet transform. Frequency-energy characteristic was analyzed depend on difference between P and S wave arrival time and noise within records. We have found that local earthquakes have similar characteristics. If frequency-energy characteristics can be found accurately, this gives us a hint to calculate P and S wave arrival time. It can be seen that wavelet transform provides successful approximation for this. In this study, 100 earthquakes with 500 records were analyzed approximately.

Keywords: Discrete Wavelet Transform, Frequency-EnergyCharacteristics, P and S waves arrival time.

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Authors: Lukas Mocek, Alexandros Markopoulos

Abstract:

The main goal of this paper is to show a possibility, how to solve numerically elliptic boundary value problems arising in 2D linear elasticity by using the fictitious domain method (FDM) and the Total-FETI domain decomposition method. We briefly mention the theoretical background of these methods and demonstrate their performance on a benchmark.

Keywords: Linear elasticity, fictitious domain method, Total-FETI, domain decomposition, saddle-point system.

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Authors: Wen-liang Chen, Peng Wei, Yidong Bao

Abstract:

This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.

Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.

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Authors: Yasunori Sugita, Toshinori Yoshikawa, Naoyuki Aikawa

Abstract:

Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied. In this paper, we propose a design method of variable FIR digital filters with an approximate linear phase characteristic in the passband. The proposed variable FIR filters have some large attenuation in stopband and their large attenuation can be varied by spectrum parameters. In the proposed design method, a quasi-equiripple characteristic can be obtained by using an iterative weighted least square method. The usefulness of the proposed design method is verified through some examples.

Keywords: Weighted Least Squares Approximation, Variable FIR Filters, Low-Delay, Quasi-Equiripple

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Authors: N. Aldea, V. Rednic, F. Matei, Tiandou Hu, M. Neumann

Abstract:

The nickel and gold nanoclusters as supported catalysts were analyzed by XAS, XRD and XPS in order to determine their local, global and electronic structure. The present study has pointed out a strong deformation of the local structure of the metal, due to its interaction with oxide supports. The average particle size, the mean squares of the microstrain, the particle size distribution and microstrain functions of the supported Ni and Au catalysts were determined by XRD method using Generalized Fermi Function for the X-ray line profiles approximation. Based on EXAFS analysis we consider that the local structure of the investigated systems is strongly distorted concerning the atomic number pairs. Metal-support interaction is confirmed by the shape changes of the probability densities of electron transitions: Ni K edge (1s → continuum and 2p), Au LIII-edge (2p3/2 → continuum, 6s, 6d5/2 and 6d3/2). XPS investigations confirm the metal-support interaction at their interface.

Keywords: local and global structure, metal-support interaction, supported metal catalysts, synchrotron radiation, X-ray absorptionspectroscopy, X-ray diffraction, X-ray photoelectron spectroscopy.

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Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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Authors: M. Zahid Hossain, M. Ashraful Amin

Abstract:

The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O(n + k) time, where k is the approximation error control parameter. The proposed algorithm is suitable for applications preferred to reduce the computation time in exchange of accuracy level such as animation and interaction in computer graphics where rapid and real-time graphics rendering is indispensable.

Keywords: Convex hull, Approximation algorithm, Computational geometry, Linear time.

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Keywords: Finite element model, model updating, modal data, optimal approximation.

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Authors: Yuichi Masukake, Yoshihisa Ishida

Abstract:

In this paper, we proposed a method to design a model-following adaptive controller for linear/nonlinear plants. Radial basis function neural networks (RBF-NNs), which are known for their stable learning capability and fast training, are used to identify linear/nonlinear plants. Simulation results show that the proposed method is effective in controlling both linear and nonlinear plants with disturbance in the plant input.

Keywords: Linear/nonlinear plants, neural networks, radial basisfunction networks.

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Authors: Hossein Kabir, Mojtaba Sadeghi

Abstract:

Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: Single-degree-of-freedom system, linear acceleration method, nonlinear excited system, equivalent displacement method.

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Authors: M-J. Huang, C-J. Huang, L-C. Chen

Abstract:

In a previously developed fast vortex method, the diffusion of the vortex sheet induced at the solid wall by the no-slip boundary conditions was modeled according to the approximation solution of Koumoutsakos and converted into discrete blobs in the vicinity of the wall. This scheme had been successfully applied to a simulation of the flow induced with an impulsively initiated circular cylinder. In this work, further modifications on this vortex method are attempted, including replacing the approximation solution by the boundary-element-method solution, incorporating a new algorithm for handling the over-weak vortex blobs, and diffusing the vortex sheet circulation in a new way suitable for high-curvature solid bodies. The accuracy is thus largely improved. The predictions of lift and drag coefficients for a uniform flow past a NASA airfoil agree well with the existing literature.

Keywords: Resurrected core-spreading vortex method, Boundaryelement method, Vortex sheet, Over-weak vortex blobs.

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Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

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Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor

Abstract:

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

Abstract:

In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.

Keywords: Non-linear vibrations, Annular plates, Large amplitudes, FGM.

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Authors: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

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Authors: N. Parandin, M. A. Fariborzi Araghi

Abstract:

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

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Authors: Soo- Young Ye, Ki-Gon Nam, Ki-Won Byun

Abstract:

In this paper, we were introduces a skin detection method using a histogram approximation based on the mean shift algorithm. The proposed method applies the mean shift procedure to a histogram of a skin map of the input image, generated by comparison with standard skin colors in the CbCr color space, and divides the background from the skin region by selecting the maximum value according to brightness level. The proposed method detects the skin region using the mean shift procedure to determine a maximum value that becomes the dividing point, rather than using a manually selected threshold value, as in existing techniques. Even when skin color is contaminated by illumination, the procedure can accurately segment the skin region and the background region. The proposed method may be useful in detecting facial regions as a pretreatment for face recognition in various types of illumination.

Keywords: Skin region detection, mean shift, histogram approximation.

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Authors: Pavel K. Lopatin, Artyom S. Yegorov

Abstract:

The Algorithm 2 for a n-link manipulator movement amidst arbitrary unknown static obstacles for a case when a sensor system supplies information about local neighborhoods of different points in the configuration space is presented. The Algorithm 2 guarantees the reaching of a target position in a finite number of steps. The Algorithm 2 is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the Algorithm2 implementation are given.

Keywords: Manipulator, trajectory planning, unknown obstacles.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, augmented linear system, nonlinear observer, formal linearization, electric power system.

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Authors: Ali Zifan, Mohammad Hassan Moradi, Sohrab Saberi, Farzad Towhidkhah

Abstract:

Electrocardiogram (ECG) segmentation is necessary to help reduce the time consuming task of manually annotating ECG-s. Several algorithms have been developed to segment the ECG automatically. We first review several of such methods, and then present a new single lead segmentation method based on Adaptive piecewise constant approximation (APCA) and Piecewise derivative dynamic time warping (PDDTW). The results are tested on the QT database. We compared our results to Laguna-s two lead method. Our proposed approach has a comparable mean error, but yields a slightly higher standard deviation than Laguna-s method.

Keywords: Adaptive Piecewise Constant Approximation, Dynamic programming, ECG segmentation, Piecewise DerivativeDynamic Time Warping.

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Authors: Muhammad Sohail Khan, Rehan Ali Shah

Abstract:

The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l₁₀, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.

Keywords: Wire coating die, Corotational Maxwell model, optimal homotopy asymptotic method, optimal homotopy perturbation method.

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Authors: Kairat T. Mynbaev, Elena N. Lomakina

Abstract:

We consider a Hardy type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion and bounds for its approximation numbers. Previously bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness have been found earlier but our approach is different in that we use domain partitions for all problems under consideration.

Keywords: Approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space.

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Authors: Ali Zifan, Sohrab Saberi, Mohammad Hassan Moradi, Farzad Towhidkhah

Abstract:

Electrocardiogram (ECG) segmentation is necessary to help reduce the time consuming task of manually annotating ECG's. Several algorithms have been developed to segment the ECG automatically. We first review several of such methods, and then present a new single lead segmentation method based on Adaptive piecewise constant approximation (APCA) and Piecewise derivative dynamic time warping (PDDTW). The results are tested on the QT database. We compared our results to Laguna's two lead method. Our proposed approach has a comparable mean error, but yields a slightly higher standard deviation than Laguna's method.

Keywords: Adaptive Piecewise Constant Approximation, Dynamic programming, ECG segmentation, Piecewise Derivative Dynamic Time Warping.

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Authors: Guangbin Wang, Deyu Sun, Fuping Tan

Abstract:

In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.

Keywords: preconditioned, MAOR method, linear system, convergence, comparison.

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Authors: Hossein Riazoshams, Midi Habshah, Jr., Mohamad Bakri Adam

Abstract:

The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers.

Keywords: Nonlinear Regression, outliers, Gradient, LeastSquare, M-estimate, MM-estimate.

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

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