Search results for: laplace approximation

Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

Keywords: Integro-differential equations, Quartic B-spline wavelet, Operational matrices.

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis.

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Authors: Ashok Kumar Goel, Suresh Chandra Saxena, Surekha Bhanot

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In this work, a Modified Functional Link Artificial Neural Network (M-FLANN) is proposed which is simpler than a Multilayer Perceptron (MLP) and improves upon the universal approximation capability of Functional Link Artificial Neural Network (FLANN). MLP and its variants: Direct Linear Feedthrough Artificial Neural Network (DLFANN), FLANN and M-FLANN have been implemented to model a simulated Water Bath System and a Continually Stirred Tank Heater (CSTH). Their convergence speed and generalization ability have been compared. The networks have been tested for their interpolation and extrapolation capability using noise-free and noisy data. The results show that M-FLANN which is computationally cheap, performs better and has greater generalization ability than other networks considered in the work.

Keywords: DLFANN, FLANN, M-FLANN, MLP

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Authors: S. Balaji, V. Swaminathan, K. Kannan

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The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: Weighted vertex cover, vertex support, approximation algorithms, NP-complete problem.

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Authors: Hassan Baghgar Bostan Abad, Ali Yazdian Varjani, Taheri Asghar

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Variable speed drives are growing and varying. Drives expanse depend on progress in different part of science like power system, microelectronic, control methods, and so on. Artificial intelligent contains hard computation and soft computation. Artificial intelligent has found high application in most nonlinear systems same as motors drive. Because it has intelligence like human but there are no sentimental against human like angriness and.... Artificial intelligent is used for various points like approximation, control, and monitoring. Because artificial intelligent techniques can use as controller for any system without requirement to system mathematical model, it has been used in electrical drive control. With this manner, efficiency and reliability of drives increase and volume, weight and cost of them decrease.

Keywords: Artificial intelligent, electrical motor, intelligent drive and control,

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Authors: S. Sukparungsee

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Generally, the traditional Shewhart p chart has been developed by for charting the binomial data. This chart has been developed using the normal approximation with condition as low defect level and the small to moderate sample size. In real applications, however, are away from these assumptions due to skewness in the exact distribution. In this paper, a modified Exponentially Weighted Moving Average (EWMA) control chat for detecting a change in binomial data by improving square root transformations, namely ISRT p EWMA control chart. The numerical results show that ISRT p EWMA chart is superior to ISRT p chart for small to moderate shifts, otherwise, the latter is better for large shifts.

Keywords: Number of defects, Exponentially Weighted Moving Average, Average Run Length, Square root transformations.

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Authors: A. Jameel, G. A. Harmain, Y. Anand, J. H. Masoodi, F. A. Najar

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The present study investigates the effect of inclusions on the shape and size of crack tip plastic zones in engineering materials subjected to static loads by employing the element free Galerkin method (EFGM). The modeling of the discontinuities produced by cracks and inclusions becomes independent of the grid chosen for analysis. The standard displacement approximation is modified by adding additional enrichment functions, which introduce the effects of different discontinuities into the formulation. The level set method has been used to represent different discontinuities present in the domain. The effect of inclusions on the extent of crack tip plastic zones is investigated by solving some numerical problems by the EFGM.

Keywords: EFGM, stress intensity factors, crack tip plastic zones, inclusions.

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Authors: Hsian Ming Goo

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The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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

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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: Pan Cheng, Jin Huang, Guang Zeng

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Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The methods possess high accuracy O(h3) and low computing complexity. The convergence and stability are proved based on Anselone-s collective compact theory. Bases on the asymptotic error expansion with odd powers, we can greatly improve the accuracy of the approximation, and also derive a posteriori error estimate which can be used for constructing self-adaptive algorithms. The efficiency of the algorithms are illustrated by numerical examples.

Keywords: boundary integral equation, extrapolation algorithm, aposteriori error estimate, elasticity.

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Authors: Duy Cuong Nguyen, Ali Makke, Guillaume Montay

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This work presents an improved single fiber pull-out test for fiber/matrix interface characterization. This test has been used to study the Inter-Facial Shear Strength ‘IFSS’ of hemp fibers reinforced polypropylene (PP). For this aim, the fiber diameter has been carefully measured using a tomography inspired method. The fiber section contour can then be approximated by a circle or a polygon. The results show that the IFSS is overestimated if the circular approximation is used. The Influence of the molding temperature on the IFSS has also been studied. We find that a molding temperature of 183◦C leads to better interfacial properties. Above or below this temperature the interface strength is reduced.

Keywords: Interface, pull-out, processing, temperature, hemp, polypropylene, composite.

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Authors: Malika.D Kedir-Talha, Mohammed Mehenni

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To improve the characterization of blood flows, we propose a method which makes it possible to use the spectral analysis of the Doppler signals. Our calculation induces a reasonable approximation, the error made on estimated speed reflects the fact that speed depends on the flow conditions as well as on measurement parameters like the bore and the volume flow rate. The estimate of the Doppler signal frequency enables us to determine the maximum Doppler frequencie Fd max as well as the maximum flow speed. The results show that the difference between the estimated frequencies ( Fde ) and the Doppler frequencies ( Fd ) is small, this variation tends to zero for important θ angles and it is proportional to the diameter D. The description of the speed of friction and the coefficient of friction justify the error rate obtained.

Keywords: Doppler frequency, Doppler spectrum, estimate speed, permanent flow.

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Authors: G. L. C. Yap

Abstract:

Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.

Keywords: Long-memory, Gaussian process, Whittle estimator, normalization, volatility, value-at-risk.

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Authors: S. Bennoud, M. Zergoug

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The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models.

The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces.

The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations.

In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: Eddy current, Finite element method, Non destructive testing, Numerical simulations.

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Authors: J. Umamaheswari, G. Radhamani

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This paper describes about the process of recognition and classification of brain images such as normal and abnormal based on PSO-SVM. Image Classification is becoming more important for medical diagnosis process. In medical area especially for diagnosis the abnormality of the patient is classified, which plays a great role for the doctors to diagnosis the patient according to the severeness of the diseases. In case of DICOM images it is very tough for optimal recognition and early detection of diseases. Our work focuses on recognition and classification of DICOM image based on collective approach of digital image processing. For optimal recognition and classification Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Support Vector Machine (SVM) are used. The collective approach by using PSO-SVM gives high approximation capability and much faster convergence.

Keywords: Recognition, classification, Relaxed Median Filter, Adaptive thresholding, clustering and Neural Networks

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Authors: Muhammad Sohail Khan, Rehan Ali Shah

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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: Zahéra Mekkioui

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Here we have considered non uniform microstrip leaky-wave antenna implemented on a dielectric waveguide by a sinusoidal profile of periodic metallic grating. The non distribution of the attenuation constant α along propagation axis, optimize the radiating characteristics and performances of such antennas. The method developped here is based on an integral method where the formalism of the admittance operator is combined to a BKW approximation. First, the effect of the modeling in the modal analysis of complex waves is studied in detail. Then, the BKW model is used for the dispersion analysis of the antenna of interest. According to antenna theory, a forced continuity of the leaky-wave magnitude at discontinuities of the non uniform structure is established. To test the validity of our dispersion analysis, computed radiation patterns are presented and compared in the millimeter band.

Keywords: antenna, leaky-wave, performances, sinusoidal.

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Authors: Anton Purnama

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Multiport diffusers are the effective engineering devices installed at the modern marine outfalls for the steady discharge of effluent streams from the coastal plants, such as municipal sewage treatment, thermal power generation and seawater desalination. A mathematical model using a two-dimensional advection-diffusion equation based on a flat seabed and incorporating the effect of a coastal tidal current is developed to calculate the compounded concentration following discharges of desalination brine from a sea outfall with multiport diffusers. The analytical solutions are computed graphically to illustrate the merging of multiple brine plumes in shallow coastal waters, and further approximation will be made to the maximum shoreline's concentration to formulate dilution of a multiport diffuser discharge.

Keywords: Desalination brine discharge, mathematical model, multiport diffuser, two sea outfalls.

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Authors: Jianqiao. Yu, Jianbo. Wang, Xinzhen. He

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This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.

Keywords: quasi-linear model, simulation, state transformation approach, the ADMIRE model.

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Authors: K. Elleuch, A. Chaari

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This paper deals with modeling and parameter identification of nonlinear systems described by Hammerstein model having Piecewise nonlinear characteristics such as Dead-zone nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the triangular basis functions leads to a particular form of Hammerstein model. The approximation by using Triangular basis functions for the description of the static nonlinear block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD) technique has been applied to separate the coupled parameters. The proposed approach has been efficiently tested on academic examples of simulation.

Keywords: Identification, Hammerstein model, Piecewisenonlinear characteristic, Dead-zone nonlinearity, Triangular basisfunctions, Singular Values Decomposition

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Authors: Karel Frana, Jianshun S. Zhang, Milos Muller

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The indoor airflow with a mixed natural/forced convection was numerically calculated using the laminar and turbulent approach. The Boussinesq approximation was considered for a simplification of the mathematical model and calculations. The results obtained, such as mean velocity fields, were successfully compared with experimental PIV flow visualizations. The effect of the distance between the cooled wall and the heat exchanger on the temperature and velocity distributions was calculated. In a room with a simple shape, the computational code OpenFOAM demonstrated an ability to numerically predict flow patterns. Furthermore, numerical techniques, boundary type conditions and the computational grid quality were examined. Calculations using the turbulence model k-omega had a significant effect on the results influencing temperature and velocity distributions.

Keywords: natural and forced convections, numerical simulations, indoor airflows.

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Authors: Yuan L. Lai, Jian H. Chen, Jui P. Hung

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Owning to the high-speed feed rate and ultra spindle speed have been used in modern machine tools, the tool-path generation plays a key role in the successful application of a High-Speed Machining (HSM) system. Because of its importance in both high-speed machining and tool-path generation, approximating a contour by NURBS format is a potential function in CAD/CAM/CNC systems. It is much more convenient to represent an ellipse by parametric form than to connect points laboriously determined in a CNC system. A new approximating method based on optimum processes and NURBS curves of any degree to the ellipses is presented in this study. Such operations can be the foundation of tool-radius compensation interpolator of NURBS curves in CNC system. All operating processes for a CAD tool is presented and demonstrated by practical models.

Keywords: Ellipse, Approximation, NURBS, Optimum.

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Authors: P. Gnanasekar, A. Nagappan, S. Sharavanan, O. Saravanan, D. Vinodkumar, T. Elayabharathi, G. Karthik

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In this paper we present the deep study about the Bio- Medical Images and tag it with some basic extracting features (e.g. color, pixel value etc). The classification is done by using a nearest neighbor classifier with various distance measures as well as the automatic combination of classifier results. This process selects a subset of relevant features from a group of features of the image. It also helps to acquire better understanding about the image by describing which the important features are. The accuracy can be improved by increasing the number of features selected. Various types of classifications were evolved for the medical images like Support Vector Machine (SVM) which is used for classifying the Bacterial types. Ant Colony Optimization method is used for optimal results. It has high approximation capability and much faster convergence, Texture feature extraction method based on Gabor wavelets etc..

Keywords: ACO Ant Colony Optimization, Correlogram, CCM Co-Occurrence Matrix, RTS Rough-Set theory

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Authors: Thi Nguyen, Lee Gordon-Brown, Jim Peterson, Peter Wheeler

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An additive fuzzy system comprising m rules with n inputs and p outputs in each rule has at least t m(2n + 2 p + 1) parameters needing to be tuned. The system consists of a large number of if-then fuzzy rules and takes a long time to tune its parameters especially in the case of a large amount of training data samples. In this paper, a new learning strategy is investigated to cope with this obstacle. Parameters that tend toward constant values at the learning process are initially fixed and they are not tuned till the end of the learning time. Experiments based on applications of the additive fuzzy system in function approximation demonstrate that the proposed approach reduces the learning time and hence improves convergence speed considerably.

Keywords: Additive fuzzy system, improving convergence, parameter learning process, unsupervised learning.

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Authors: Dylan M. Copeland

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We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Tusharkanta Das, Tumbanath Samantara, Sukanta Kumar Sahoo

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Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.

Keywords: Heat transfer, radiation, MHD, free convection, porous medium, suction.

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Authors: M. S. Annie Christi

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Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: Best candidates method, centroid ranking technique, robust ranking technique, transportation problem, fuzzy transportation problem.

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Authors: Anatoli Torokhti, Phil Howlett

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We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.

Keywords: stochastic signals, optimization problems in signal processing.

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Authors: Anatoli Torokhti, Phil Howlett

Abstract:

A theory for optimal filtering of infinite sets of random signals is presented. There are several new distinctive features of the proposed approach. First, a single optimal filter for processing any signal from a given infinite signal set is provided. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the scheme concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.

Keywords: Optimal filtering, data compression, stochastic signals.

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Authors: U. C. Amadi, N. A. Udoh

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One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.

Keywords: Ying Buzu Shu, nonlinear boundary problem, Taylor series algorithm, infinite series.

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