Search results for: Padé approximation

Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal that the HPM with the enhancement of PA is a very effective, convenient and quite accurate to such types of partial differential equations.

Keywords: Homotopy perturbation method, Padé approximants, cubic Boussinesq equation, modified Boussinesq equation.

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Authors: Jay Singh, Kalyan Chatterjee, C. B. Vishwakarma

Abstract:

A mixed method by combining a Eigen algorithm and improved pade approximations is proposed for reducing the order of the large-scale dynamic systems. The most dominant Eigen value of both original and reduced order systems remain same in this method. The proposed method guarantees stability of the reduced model if the original high-order system is stable and is comparable in quality with the other well known existing order reduction methods. The superiority of the proposed method is shown through examples taken from the literature.

Keywords: Eigen algorithm, Order reduction, improved pade approximations, Stability, Transfer function.

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Authors: J. Kavikumar, N. S. Manian, M.B.K. Moorthy

Abstract:

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

Keywords: Fuzzy best co-approximation, fuzzy quotient spaces, proximinality, Chebyshevity, best simultaneous co-approximation.

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Authors: Xun Ge, Zhaowen Li

Abstract:

Covering approximation spaces is a class of important generalization of approximation spaces. For a subset X of a covering approximation space (U, C), is X definable or rough? The answer of this question is uncertain, which depends on covering approximation operators endowed on (U, C). Note that there are many various covering approximation operators, which can be endowed on covering approximation spaces. This paper investigates covering approximation spaces endowed ten covering approximation operators respectively, and establishes some relations among definable subsets, inner definable subsets and outer definable subsets in covering approximation spaces, which deepens some results on definable subsets in approximation spaces.

Keywords: Covering approximation space, covering approximation operator, definable subset, inner definable subset, outer definable subset.

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Authors: C.B. Vishwakarma

Abstract:

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

Keywords: Modified pole clustering, order reduction, padeapproximation, stability, transfer function.

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Authors: Mei He, Ying Ge, Jingyu Qian

Abstract:

Let (U;D) be a Gr-covering approximation space (U; C) with covering lower approximation operator D and covering upper approximation operator D. For a subset X of U, this paper investigates the following three conditions: (1) X is a definable subset of (U;D); (2) X is an inner definable subset of (U;D); (3) X is an outer definable subset of (U;D). It is proved that if one of the above three conditions holds, then the others hold. These results give a positive answer of an open problem for definable subsets of covering approximation spaces.

Keywords: Covering approximation space, covering approximation operator, definable subset, inner definable subset, outer definable subset.

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Authors: Wajdi Bellil, Chokri Ben Amar, Adel M. Alimi

Abstract:

This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn - R from scattered samples (xi; y = f(xi)) i=1....n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate f as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.

Keywords: Beta wavelets networks, RBF neural network, training algorithms, MSE, 1-D, 2D function approximation.

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Authors: Xun Ge, Jinjin Li, Ying Ge

Abstract:

Adopting Zakowski-s upper approximation operator C and lower approximation operator C, this paper investigates granularity-wise separations in covering approximation spaces. Some characterizations of granularity-wise separations are obtained by means of Pawlak rough sets and some relations among granularitywise separations are established, which makes it possible to research covering approximation spaces by logical methods and mathematical methods in computer science. Results of this paper give further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

Keywords: Rough set, covering approximation space, granularitywise separation.

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Authors: A. A. Penin

Abstract:

An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.

Keywords: a solar cell generator, I − V characteristic, p − n junction, approximation

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Authors: Anirudha Narain, Dinesh Chandra, Ravindra K. S.

Abstract:

A computationally simple approach of model order reduction for single input single output (SISO) and linear timeinvariant discrete systems modeled in frequency domain is proposed in this paper. Denominator of the reduced order model is determined using fuzzy C-means clustering while the numerator parameters are found by matching time moments and Markov parameters of high order system.

Keywords: Model Order reduction, Discrete-time system, Fuzzy C-Means Clustering, Padé approximation.

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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: 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: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.

Keywords: Electrically conducting elastico-viscous fluid, symmetry solution, Homotopy perturbation method, Padé approximation, 4th order Runge–Kutta, Maple

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Authors: Mario Mastriani

Abstract:

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.

Keywords: Compression, denoising, projections, wavelets.

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Authors: S. B. Mansuri

Abstract:

In this paper, at first we explain about negative hypergeometric distribution and its properties. Then we use the w-function and the Stein identity to give a result on the poisson approximation to the negative hypergeometric distribution in terms of the total variation distance between the negative hypergeometric and poisson distributions and its upper bound.

Keywords: Negative hypergeometric distribution, Poisson distribution, Poisson approximation, Stein-Chen identity, w-function.

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Authors: Yongxin Yuan, Hao Liu

Abstract:

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

Keywords: Inverse problem, Least-squares solution, model updating, Singular value decomposition (SVD), Optimal approximation.

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Authors: A.S. Rebaï, M. Elloumi

Abstract:

The Shortest Approximate Common Superstring (SACS) problem is : Given a set of strings f={w1, w2, ... , wn}, where no wi is an approximate substring of wj, i ≠ j, find a shortest string Sa, such that, every string of f is an approximate substring of Sa. When the number of the strings n>2, the SACS problem becomes NP-complete. In this paper, we present a greedy approximation SACS algorithm. Our algorithm is a 1/2-approximation for the SACS problem. It is of complexity O(n2*(l2+log(n))) in computing time, where n is the number of the strings and l is the length of a string. Our SACS algorithm is based on computation of the Length of the Approximate Longest Overlap (LALO).

Keywords: Shortest approximate common superstring, approximation algorithms, strings overlaps, complexities.

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Authors: Properties, Approximation Distribution Reductions in Multigranulation Rough Set Model

Abstract:

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

Keywords: Incomplete information system, maximal compatible class, multi-granulation rough set model, reduction.

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Authors: Jevgenijs Carkovs

Abstract:

The paper is devoted to stochastic analysis of finite dimensional difference equation with dependent on ergodic Markov chain increments, which are proportional to small parameter ". A point-form solution of this difference equation may be represented as vertexes of a time-dependent continuous broken line given on the segment [0,1] with "-dependent scaling of intervals between vertexes. Tending " to zero one may apply stochastic averaging and diffusion approximation procedures and construct continuous approximation of the initial stochastic iterations as an ordinary or stochastic Ito differential equation. The paper proves that for sufficiently small " these equations may be successfully applied not only to approximate finite number of iterations but also for asymptotic analysis of iterations, when number of iterations tends to infinity.

Keywords: Markov dynamical system, diffusion approximation, equilibrium stochastic stability.

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Authors: Kaushalendra K. Khadanga, Lee Hee Hyol

Abstract:

Passenger comfort has been paramount in the design of suspension systems of high speed cars. To analyze the effect of vibration on vehicle ride quality, a vertical model of a six degree of freedom railway passenger vehicle, with front and rear suspension, is built. It includes car body flexible effects and vertical rigid modes. A second order linear shaping filter is constructed to model Gaussian white noise into random rail excitation. The temporal correlation between the front and rear wheels is given by a second order Pade approximation. The complete track and the vehicle model are then designed. An active secondary suspension system based on a Linear Quadratic Gaussian (LQG) optimal control method is designed. The results show that the LQG control method reduces the vertical acceleration, pitching acceleration and vertical bending vibration of the car body as compared to the passive system.

Keywords: Active suspension, bending vibration, railway vehicle, vibration control.

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Authors: S. Heydarzadeh, A. Kadivarian, P. Torkzadeh

Abstract:

Implemented 5-bit 125-MS/s successive approximation register (SAR) analog to digital converter (ADC) on FPGA is presented in this paper.The design and modeling of a high performance SAR analog to digital converter are based on monotonic capacitor switching procedure algorithm .Spartan 3 FPGA is chosen for implementing SAR analog to digital converter algorithm. SAR VHDL program writes in Xilinx and modelsim uses for showing results.

Keywords: Analog to digital converter, Successive approximation, Capacitor switching algorithm, FPGA

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Authors: S. Panda, S. K. Tomar, R. Prasad, C. Ardil

Abstract:

Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.

Keywords: Model Order Reduction, Markov Parameters, Routh Approximation, Particle Swarm Optimization, Integral Squared Error, Steady State Stability.

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Authors: Yeonsoo Jang, Dongweon Yoon, Ki Ho Kwon, Jaeyoon Lee, Wooju Lee

Abstract:

Phase error in communications systems degrades error performance. In this paper, we present a simple approximation for the average error probability of the binary phase shift keying (BPSK) in the presence of phase error having a uniform distribution on arbitrary intervals. For the simple approximation, we use symmetry and periodicity of a sinusoidal function. Approximate result for the average error probability is derived, and the performance is verified through comparison with simulation result.

Keywords: Average error probability, Phase shift keying, Phase error

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Authors: S. Seyedtabaii, E. Seyedtabaii

Abstract:

Rounding of coefficients is a common practice in hardware implementation of digital filters. Where some coefficients are very close to zero or one, as assumed in this paper, this rounding action also leads to some computation reduction. Furthermore, if the discarded coefficient is of high order, a reduced order filter is obtained, otherwise the order does not change but computation is reduced. In this paper, the Least Squares approximation to rounded (or discarded) coefficient FIR filter is investigated. The result also succinctly extended to general type of FIR filters.

Keywords: Digital filter, filter approximation, least squares, model order reduction.

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

Abstract:

This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions.

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Authors: Sirapat Lookrak, Anol Paisal

Abstract:

Space debris has numerous manifestations including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane so the Gaussian surface is a very small cylinder and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless manoeuvring space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

Keywords: Near-field approximation, far-field approximation, localized Gauss’s law, electric charge density.

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Authors: Edlira Donefski, Lorenc Ekonomi, Tina Donefski

Abstract:

Edgeworth approximation is one of the most important statistical methods that has a considered contribution in the reduction of the sum of standard deviation of the independent variables’ coefficients in a Quantile Regression Model. This model estimates the conditional median or other quantiles. In this paper, we have applied approximating statistical methods in an economical problem. We have created and generated a quantile regression model to see how the profit gained is connected with the realized sales of the cosmetic products in a real data, taken from a local business. The Linear Regression of the generated profit and the realized sales was not free of autocorrelation and heteroscedasticity, so this is the reason that we have used this model instead of Linear Regression. Our aim is to analyze in more details the relation between the variables taken into study: the profit and the finalized sales and how to minimize the standard errors of the independent variable involved in this study, the level of realized sales. The statistical methods that we have applied in our work are Edgeworth Approximation for Independent and Identical distributed (IID) cases, Bootstrap version of the Model and the Edgeworth approximation for Bootstrap Quantile Regression Model. The graphics and the results that we have presented here identify the best approximating model of our study.

Keywords: Bootstrap, Edgeworth approximation, independent and Identical distributed, quantile.

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Authors: Erol Seke, Kemal Özkan

Abstract:

Linear approximation of point spread function (PSF) is a new method for determining subpixel translations between images. The problem with the actual algorithm is the inability of determining translations larger than 1 pixel. In this paper a multiresolution technique is proposed to deal with the problem. Its performance is evaluated by comparison with two other well known registration method. In the proposed technique the images are downsampled in order to have a wider view. Progressively decreasing the downsampling rate up to the initial resolution and using linear approximation technique at each step, the algorithm is able to determine translations of several pixels in subpixel levels.

Keywords: Point Spread Function, Subpixel translation, Superresolution, Multiresolution approach.

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Authors: Yasunori Sugita, Toshinori Yoshikawa

Abstract:

The design problem of Infinite Impulse Response (IIR) digital filters is usually expressed as the minimization problem of the complex magnitude error that includes both the magnitude and phase information. However, the group delay of the filter obtained by solving such design problem may be far from the desired group delay. In this paper, we propose a design method of stable IIR digital filters with prespecified maximum group delay errors. In the proposed method, the approximation problems of the magnitude-phase and group delay are separately defined, and these two approximation problems are alternately solved using successive projections. As a result, the proposed method can design the IIR filters that satisfy the prespecified allowable errors for not only the complex magnitude but also the group delay by alternately executing the coefficient update for the magnitude-phase and the group delay approximation. The usefulness of the proposed method is verified through some examples.

Keywords: Filter design, Group delay approximation, Stable IIRfilters, Successive projection method.

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Authors: E. Assareh, M.A. Behrang, M. Ghalambaz, A.R. Noghrehabadi, A. Ghanbarzadeh

Abstract:

In this paper, a new approach is introduced to solve Blasius equation using parameter identification of a nonlinear function which is used as approximation function. Bees Algorithm (BA) is applied in order to find the adjustable parameters of approximation function regarding minimizing a fitness function including these parameters (i.e. adjustable parameters). These parameters are determined how the approximation function has to satisfy the boundary conditions. In order to demonstrate the presented method, the obtained results are compared with another numerical method. Present method can be easily extended to solve a wide range of problems.

Keywords: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

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