Search results for: Asymptotic error constant

Authors: Young Hee Geum

Abstract:

We propose the numerical method defined by

xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N,

and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: Asymptotic error constant, iterative method , multiple root, root-finding.

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Authors: Tapas Kumar Sinha, Joseph Mathew

Abstract:

Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).

Keywords: KdV equation, Asymptotic Degeneracy, Solitons, Inverse Scattering

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

Abstract:

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: M. Siosemarde, F. Kave, E. Pazira, H. Sedghi, S. J. Ghaderi

Abstract:

Salinity is a measure of the amount of salts in the water. Total Dissolved Solids (TDS) as salinity parameter are often determined using laborious and time consuming laboratory tests, but it may be more appropriate and economical to develop a method which uses a more simple soil salinity index. Because dissolved ions increase salinity as well as conductivity, the two measures are related. The aim of this research was determine of constant coefficients for predicting of Total Dissolved Solids (TDS) based on Electrical Conductivity (EC) with Statistics of Correlation coefficient, Root mean square error, Maximum error, Mean Bias error, Mean absolute error, Relative error and Coefficient of residual mass. For this purpose, two experimental areas (S1, S2) of Khuzestan province-IRAN were selected and four treatments with three replications by series of double rings were applied. The treatments were included 25cm, 50cm, 75cm and 100cm water application. The results showed the values 16.3 & 12.4 were the best constant coefficients for predicting of Total Dissolved Solids (TDS) based on EC in Pilot S1 and S2 with correlation coefficient 0.977 & 0.997 and 191.1 & 106.1 Root mean square errors (RMSE) respectively.

Keywords: constant coefficients, electrical conductivity, Khuzestan plain and total dissolved solids.

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Authors: Hsuan-Ku Liu

Abstract:

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Hsuan-Ku Liu, Ming Long Liu

Abstract:

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

Abstract:

In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.

Keywords: Hopfield neural networks, uniform asymptotic stability, global asymptotic stability, exponential stability.

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Authors: R. Sabre, W. Horrigue, J. C. Simon

Abstract:

This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.

Keywords: Spectral density, stable processes, aliasing, periodogram.

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Authors: Pan Cheng, Jin Huang, Guang Zeng

Abstract:

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: 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: Qianhong Zhang, Wenzhuan Zhang

Abstract:

This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.

Keywords: Difference equations, stability, unstable, global asymptotic behavior.

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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Authors: Shuting Ji, Yueming Zhang, Jing Zhao

Abstract:

The output error of the globoidal cam mechanism can be considered as a relevant indicator of mechanism performance, because it determines kinematic and dynamical behavior of mechanical transmission. Based on the differential geometry and the rigid body transformations, the mathematical model of surface geometry of the globoidal cam is established. Then we present the analytical expression of the output error (including the transmission error and the displacement error along the output axis) by considering different manufacture and assembly errors. The effects of the center distance error, the perpendicular error between input and output axes and the rotational angle error of the globoidal cam on the output error are systematically analyzed. A globoidal cam mechanism which is widely used in automatic tool changer of CNC machines is applied for illustration. Our results show that the perpendicular error and the rotational angle error have little effects on the transmission error but have great effects on the displacement error along the output axis. This study plays an important role in the design, manufacture and assembly of the globoidal cam mechanism.

Keywords: Globoidal cam mechanism, manufacture error, transmission error, automatic tool changer.

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Authors: Carolina B. Baguio

Abstract:

One of the purposes of the robust method of estimation is to reduce the influence of outliers in the data, on the estimates. The outliers arise from gross errors or contamination from distributions with long tails. The trimmed mean is a robust estimate. This means that it is not sensitive to violation of distributional assumptions of the data. It is called an adaptive estimate when the trimming proportion is determined from the data rather than being fixed a “priori-. The main objective of this study is to find out the robustness properties of the adaptive trimmed means in terms of efficiency, high breakdown point and influence function. Specifically, it seeks to find out the magnitude of the trimming proportion of the adaptive trimmed mean which will yield efficient and robust estimates of the parameter for data which follow a modified Weibull distribution with parameter λ = 1/2 , where the trimming proportion is determined by a ratio of two trimmed means defined as the tail length. Secondly, the asymptotic properties of the tail length and the trimmed means are also investigated. Finally, a comparison is made on the efficiency of the adaptive trimmed means in terms of the standard deviation for the trimming proportions and when these were fixed a “priori". The asymptotic tail lengths defined as the ratio of two trimmed means and the asymptotic variances were computed by using the formulas derived. While the values of the standard deviations for the derived tail lengths for data of size 40 simulated from a Weibull distribution were computed for 100 iterations using a computer program written in Pascal language. The findings of the study revealed that the tail lengths of the Weibull distribution increase in magnitudes as the trimming proportions increase, the measure of the tail length and the adaptive trimmed mean are asymptotically independent as the number of observations n becomes very large or approaching infinity, the tail length is asymptotically distributed as the ratio of two independent normal random variables, and the asymptotic variances decrease as the trimming proportions increase. The simulation study revealed empirically that the standard error of the adaptive trimmed mean using the ratio of tail lengths is relatively smaller for different values of trimming proportions than its counterpart when the trimming proportions were fixed a 'priori'.

Keywords: Adaptive robust estimate, asymptotic efficiency, breakdown point, influence function, L-estimates, location parameter, tail length, Weibull distribution.

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

Abstract:

The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

Abstract:

In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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Authors: Daohong Yang, Xiang Zhang, Wanting Zhou, Lei Li

Abstract:

Visual Simultaneous Localization and Mapping (VSLAM) is a technology that gathers information about the surrounding environment to ascertain its own position and create a map. It is widely used in computer vision, robotics, and various other fields. Many visual SLAM systems, such as OBSLAM3, utilize a constant velocity motion model. The utilization of this model facilitates the determination of the initial pose of the current frame, thereby enhancing the efficiency and precision of feature matching. However, it is often difficult to satisfy the constant velocity motion model in actual situations. This can result in a significant deviation between the obtained initial pose and the true value, leading to errors in nonlinear optimization results. Therefore, this paper proposes a motion model based on acceleration that can be applied to most SLAM systems. To provide a more accurate description of the camera pose acceleration, we separate the pose transformation matrix into its rotation matrix and translation vector components. The rotation matrix is now represented by a rotation vector. We assume that, over a short period, the changes in rotating angular velocity and translation vector remain constant. Based on this assumption, the initial pose of the current frame is estimated. In addition, the error of the constant velocity model is analyzed theoretically. Finally, we apply our proposed approach to the ORBSLAM3 system and evaluate two sets of sequences from the TUM datasets. The results show that our proposed method has a more accurate initial pose estimation, resulting in an improvement of 6.61% and 6.46% in the accuracy of the ORBSLAM3 system on the two test sequences, respectively.

Keywords: Error estimation, constant acceleration motion model, pose estimation, visual SLAM.

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Authors: S. Cherif, S. Marcos, M. Jaidane

Abstract:

In this paper the behavior of the decision feedback equalizers (DFEs) adapted by the decision-directed or the constant modulus blind algorithms is presented. An analysis of the error surface of the corresponding criterion cost functions is first developed. With the intention of avoiding the ill-convergence of the algorithm, the paper proposes to modify the shape of the cost function error surface by using a soft decision instead of the hard one. This was shown to reduce the influence of false decisions and to smooth the undesirable minima. Modified algorithms using the soft decision during a pseudo-training phase with an automatic switch to the properly tracking phase are then derived. Computer simulations show that these modified algorithms present better ability to avoid local minima than conventional ones.

Keywords: Blind DFEs, decision-directed algorithm, constant modulus algorithm, cost function analysis, convergence analysis, soft decision.

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Authors: E. Arsuaga Uriarte, F. Díaz Martín

Abstract:

The SOM has several beneficial features which make it a useful method for data mining. One of the most important features is the ability to preserve the topology in the projection. There are several measures that can be used to quantify the goodness of the map in order to obtain the optimal projection, including the average quantization error and many topological errors. Many researches have studied how the topology preservation should be measured. One option consists of using the topographic error which considers the ratio of data vectors for which the first and second best BMUs are not adjacent. In this work we present a study of the behaviour of the topographic error in different kinds of maps. We have found that this error devaluates the rectangular maps and we have studied the reasons why this happens. Finally, we suggest a new topological error to improve the deficiency of the topographic error.

Keywords: Map lattice, Self-Organizing Map, topographic error, topology preservation.

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Authors: Vinita V. Sondur, Vilas B. Sondur, Narasimha H. Ayachit

Abstract:

It is observed that the Weighted least-square (WLS) technique, including the modifications, results in equiripple error curve. The resultant error as a percent of the ideal value is highly non-uniformly distributed over the range of frequencies for which the differentiator is designed. The present paper proposes a modification to the technique so that the optimization procedure results in lower maximum relative error compared to the ideal values. Simulation results for first order as well as higher order differentiators are given to illustrate the excellent performance of the proposed method.

Keywords: Differentiator, equiripple, error distribution, relative error.

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Authors: Thuraya M. Qaradaghi, Newroz N. Abdulrazaq

Abstract:

The McEliece cryptosystem is an asymmetric type of cryptography based on error correction code. The classical McEliece used irreducible binary Goppa code which considered unbreakable until now especially with parameter [1024, 524, and 101], but it is suffering from large public key matrix which leads to be difficult to be used practically. In this work Irreducible and Separable Goppa codes have been introduced. The Irreducible and Separable Goppa codes used are with flexible parameters and dynamic error vectors. A Comparison between Separable and Irreducible Goppa code in McEliece Cryptosystem has been done. For encryption stage, to get better result for comparison, two types of testing have been chosen; in the first one the random message is constant while the parameters of Goppa code have been changed. But for the second test, the parameters of Goppa code are constant (m=8 and t=10) while the random message have been changed. The results show that the time needed to calculate parity check matrix in separable are higher than the one for irreducible McEliece cryptosystem, which is considered expected results due to calculate extra parity check matrix in decryption process for g2(z) in separable type, and the time needed to execute error locator in decryption stage in separable type is better than the time needed to calculate it in irreducible type. The proposed implementation has been done by Visual studio C#.

Keywords: McEliece cryptosystem, Goppa code, separable, irreducible.

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Authors: Alessandro Barbiero

Abstract:

In this paper some procedures for building confidence intervals for the reliability in stress-strength models are discussed and empirically compared. The particular case of a bivariate normal setup is considered. The confidence intervals suggested are obtained employing approximations or asymptotic properties of maximum likelihood estimators. The coverage and the precision of these intervals are empirically checked through a simulation study. An application to real paired data is also provided.

Keywords: Approximate estimators, asymptotic theory, confidence interval, Monte Carlo simulations, stress-strength, variance estimation.

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Authors: Sang-Chul Kim, Sung-Il Chien

Abstract:

The error diffusion method generates worm artifacts, and weakens the edge of the halftone image when the continuous gray scale image is reproduced by a binary image. First, to enhance the edges, we propose the edge-enhancing filter by considering the quantization error information and gradient of the neighboring pixels. Furthermore, to remove worm artifacts often appearing in a halftone image, we add adaptively random noise into the weights of an error filter.

Keywords: Artifact suppression, Edge enhancement, Error diffusion method, Halftone image

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Authors: J. Tonkonogij, A. Pedišius, A. Stankevičius

Abstract:

The new semi-experimental method for simulation of the turbine flow meters rotation in the transitional flow has been developed. The method is based on the experimentally established exponential low of changing of dimensionless relative turbine gas meter rotation frequency and meter inertia time constant. For experimental evaluation of the meter time constant special facility has been developed. The facility ensures instant switching of turbine meter under test from one channel to the other channel with different flow rate and measuring the meter response. The developed method can be used for evaluation and predication of the turbine meters response and dynamic error in the transitional flow with any arbitrary law of flow rate changing. The examples of the method application are presented.

Keywords: Dynamic error, pulsing flow, numerical simulation, response, turbine gas meters.

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Authors: Andrey V. Timofeev, Dmitry V. Egorov

Abstract:

The practical efficient approach is suggested for estimation of the seismoacoustic sources energy in C-OTDR monitoring systems. This approach is represents the sequential plan for confidence estimation both the seismoacoustic sources energy, as well the absorption coefficient of the soil. The sequential plan delivers the non-asymptotic guaranteed accuracy of obtained estimates in the form of non-asymptotic confidence regions with prescribed sizes. These confidence regions are valid for a finite sample size when the distributions of the observations are unknown. Thus, suggested estimates are non-asymptotic and nonparametric, and also these estimates guarantee the prescribed estimation accuracy in form of prior prescribed size of confidence regions, and prescribed confidence coefficient value.

Keywords: C-OTDR-system, guaranteed estimates, nonparametric estimation, sequential confidence estimation, multichannel monitoring systems.

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Authors: Payam Haghparast, Mikhail V. Sorin, Hakim Nesreddine

Abstract:

The complex oblique shock phenomenon can be simply assumed as a normal shock at the constant area section to simulate a sharp pressure increase and velocity decrease in 1-D thermodynamic models. The assumed normal shock location is one of the greatest sources of error in ejector thermodynamic models. Most researchers consider an arbitrary location without justifying it. Our study compares the effect of normal shock place on ejector dimensions in 1-D models. To this aim, two different ejector experimental test benches, a constant area-mixing ejector (CAM) and a constant pressure-mixing (CPM) are considered, with different known geometries, operating conditions and working fluids (R245fa, R141b). In the first step, in order to evaluate the real value of the efficiencies in the different ejector parts and critical back pressure, a CFD model was built and validated by experimental data for two types of ejectors. These reference data are then used as input to the 1D model to calculate the lengths and the diameters of the ejectors. Afterwards, the design output geometry calculated by the 1D model is compared directly with the corresponding experimental geometry. It was found that there is a good agreement between the ejector dimensions obtained by the 1D model, for both CAM and CPM, with experimental ejector data. Furthermore, it is shown that normal shock place affects only the constant area length as it is proven that the inlet normal shock assumption results in more accurate length. Taking into account previous 1D models, the results suggest the use of the assumed normal shock location at the inlet of the constant area duct to design the supersonic ejectors.

Keywords: 1D model, constant area-mixing, constant pressure-mixing, normal shock location, ejector dimensions.

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Authors: Peter U. Eze, P. Udaya, Robin J. Evans

Abstract:

Data hiding can be achieved by Steganography or invisible digital watermarking. For digital watermarking, both accurate retrieval of the embedded watermark and the integrity of the cover image are important. Medical image security in Teleradiology is one of the applications where the embedded patient record needs to be extracted with accuracy as well as the medical image integrity verified. In this research paper, the Constant Correlation Spread Spectrum digital watermarking for medical image tamper detection and accurate embedded watermark retrieval is introduced. In the proposed method, a watermark bit from a patient record is spread in a medical image sub-block such that the correlation of all watermarked sub-blocks with a spreading code, W, would have a constant value, p. The constant correlation p, spreading code, W and the size of the sub-blocks constitute the secret key. Tamper detection is achieved by flagging any sub-block whose correlation value deviates by more than a small value, ℇ, from p. The major features of our new scheme include: (1) Improving watermark detection accuracy for high-pixel depth medical images by reducing the Bit Error Rate (BER) to Zero and (2) block-level tamper detection in a single computational process with simultaneous watermark detection, thereby increasing utility with the same computational cost.

Keywords: Constant correlation, medical image, spread spectrum, tamper detection, watermarking.

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Authors: Yung-Yuan Hsu

Abstract:

The primary objective of this paper was to construct a “kinematic parameter-independent modeling of three-axis machine tools for geometric error measurement" technique. Improving the accuracy of the geometric error for three-axis machine tools is one of the machine tools- core techniques. This paper first applied the traditional method of HTM to deduce the geometric error model for three-axis machine tools. This geometric error model was related to the three-axis kinematic parameters where the overall errors was relative to the machine reference coordinate system. Given that the measurement of the linear axis in this model should be on the ideal motion axis, there were practical difficulties. Through a measurement method consolidating translational errors and rotational errors in the geometric error model, we simplified the three-axis geometric error model to a kinematic parameter-independent model. Finally, based on the new measurement method corresponding to this error model, we established a truly practical and more accurate error measuring technique for three-axis machine tools.

Keywords: Three-axis machine tool, Geometric error, HTM, Error measuring

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Authors: M. T. Anwar, P. K. Lala, P. Thenappan

Abstract:

This paper presents the decoder design for the single error correcting and double error detecting code proposed by the authors in an earlier paper. The speed of error detection and correction of a code is largely dependent upon the associated encoder and decoder circuits. The complexity and the speed of such circuits are determined by the number of 1?s in the parity check matrix (PCM). The number of 1?s in the parity check matrix for the code proposed by the authors are fewer than in any currently known single error correcting/double error detecting code. This results in simplified encoding and decoding circuitry for error detection and correction.

Keywords: Decoder, Hsiao code, Parity Check Matrix, Syndrome Pattern.

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