Search results for: Volume of Fluid (VOF) method.

Authors: Tarifa S. Almulhim, Ludmil Mikhailov, Dong-Ling Xu

Abstract:

In this paper, a method for deriving a group priority vector in the Fuzzy Analytic Network Process (FANP) is proposed. By introducing importance weights of multiple decision makers (DMs) based on their experiences, the Fuzzy Preferences Programming Method (FPP) is extended to a fuzzy group prioritization problem in the FANP. Additionally, fuzzy pair-wise comparison judgments are presented rather than exact numerical assessments in order to model the uncertainty and imprecision in the DMs- judgments and then transform the fuzzy group prioritization problem into a fuzzy non-linear programming optimization problem which maximize the group satisfaction. Unlike the known fuzzy prioritization techniques, the new method proposed in this paper can easily derive crisp weights from incomplete and inconsistency fuzzy set of comparison judgments and does not require additional aggregation producers. Detailed numerical examples are used to illustrate the implement of our approach and compare with the latest fuzzy prioritization method.

Keywords: Fuzzy Analytic Network Process (FANP), Fuzzy Non-linear Programming, Fuzzy Preferences Programming Method (FPP), Multiple Criteria Decision-Making (MCDM), Triangular Fuzzy Number.

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Authors: Sambit Prasad Kar, P.Palanisamy

Abstract:

In this paper a novel method for multiple one dimensional real valued sinusoidal signal frequency estimation in the presence of additive Gaussian noise is postulated. A computationally simple frequency estimation method with efficient statistical performance is attractive in many array signal processing applications. The prime focus of this paper is to combine the subspace-based technique and a simple peak search approach. This paper presents a variant of the Propagator Method (PM), where a collaborative approach of SUMWE and Propagator method is applied in order to estimate the multiple real valued sine wave frequencies. A new data model is proposed, which gives the dimension of the signal subspace is equal to the number of frequencies present in the observation. But, the signal subspace dimension is twice the number of frequencies in the conventional MUSIC method for estimating frequencies of real-valued sinusoidal signal. The statistical analysis of the proposed method is studied, and the explicit expression of asymptotic (large-sample) mean-squared-error (MSE) or variance of the estimation error is derived. The performance of the method is demonstrated, and the theoretical analysis is substantiated through numerical examples. The proposed method can achieve sustainable high estimation accuracy and frequency resolution at a lower SNR, which is verified by simulation by comparing with conventional MUSIC, ESPRIT and Propagator Method.

Keywords: Frequency estimation, peak search, subspace-based method without eigen decomposition, quadratic convex function.

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Authors: O. Younis, J. Pallares, F. X. Grau

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This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water solution 50%). The simulations are performed at two different Rayleigh numbers (5·106 and 5·107) and six different Prandtl numbers (3 · 105 ≥Pr≥ 50). Heat conduction through the cavity glass walls is also considered. The propsed correlations of the averaged heat transfer coefficient (N u) showed that it is dependant on the initial Ra and almost independent on P r. The instantaneous flow patterns, temperature contours and time evolution of volume averaged temperature and heat transfer coefficient are presented and analyzed.

Keywords: Transient natural convection, High Prandtl number, variable viscosity.

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Authors: Samy Sadek, Ayoub Al-Hamadi, Bernd Michaelis, Usama Sayed

Abstract:

In this paper, we propose a supervised method for color image classification based on a multilevel sigmoidal neural network (MSNN) model. In this method, images are classified into five categories, i.e., “Car", “Building", “Mountain", “Farm" and “Coast". This classification is performed without any segmentation processes. To verify the learning capabilities of the proposed method, we compare our MSNN model with the traditional Sigmoidal Neural Network (SNN) model. Results of comparison have shown that the MSNN model performs better than the traditional SNN model in the context of training run time and classification rate. Both color moments and multi-level wavelets decomposition technique are used to extract features from images. The proposed method has been tested on a variety of real and synthetic images.

Keywords: Image classification, multi-level neural networks, feature extraction, wavelets decomposition.

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Authors: Z. Pavlík, J. Fořt, J. Žumár, M. Pavlíková, R. Černý

Abstract:

The cup method is applied for the measurement of water vapor transport properties of porous materials worldwide. However, in practical applications the experimental results are often used without taking into account some secondary effects which can play an important role under specific conditions. In this paper, the effect of temperature on water vapor transport properties of cellular concrete is studied, together with the influence of sample thickness. At first, the bulk density, matrix density, total open porosity and sorption and desorption isotherms are measured for material characterization purposes. Then, the steady state cup method is used for determination of water vapor transport properties, whereas the measurements are performed at several temperatures and for three different sample thicknesses.

Keywords: Water vapor transport, cellular concrete, cup method, temperature, sample thickness.

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Authors: Seyed Mohammad Hosseini, Amirhossein Moghanian

Abstract:

The main purpose of this research was to design a biomimetic system by freeze-drying method for evaluating the effect of adding 5 and 10 mol. % of zinc (Zn) in 58S bioactive glass and gelatin (5ZnBG/G and 10ZnBG/G) in terms of structural and biological changes. The structural analyses of samples were performed by X-Ray Diffraction (XRD), scanning electron microscopy (SEM) and Fourier-transform infrared (FTIR) spectroscopy. Also, 3-(4,5dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) and alkaline phosphatase (ALP) activity tests were carried out for investigation of MC3T3-E1 cell behaviors. The SEM results demonstrated the spherical shape of the formed hydroxyapatite (HA) phases and also HA characteristic peaks were detected by XRD spectroscopy after 3 days of immersion in the simulated body fluid (SBF) solution. Meanwhile, FTIR spectra proved that the intensity of P–O peaks for 5ZnBG/G was more than 10ZnBG/G and control samples. Moreover, the results of ALP activity test illustrated that the optimal amount of Zn (5ZnBG/G) caused a considerable enhancement in bone cell growth. Taken together, the scaffold with 5 mol.% Zn was introduced as an optimal sample because of its higher biocompatibility, in vitro bioactivity and growth of MC3T3-E1 cells in comparison with other samples in bone tissue engineering.

Keywords: Scaffold, gelatin, modified bioactive glass, ALP, bone tissue engineering.

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Authors: M. Victor Jose, V. Seenivasagam

Abstract:

This paper describes a logical method to enhance security on the grid computing to restrict the misuse of the grid resources. This method is an economic and efficient one to avoid the usage of the special devices. The security issues, techniques and solutions needed to provide a secure grid computing environment are described. A well defined process for security management among the resource accesses and key holding algorithm is also proposed. In this method, the identity management, access control and authorization and authentication are effectively handled.

Keywords: Grid security, Irregular binary series, Key holding mechanism, Resource identity, Secure resource access.

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Authors: Haydar Kepekçi, Baha Zafer, Hasan Rıza Güven

Abstract:

Noise disturbance is one of the major factors considered in the fast development of aircraft technology. This paper reviews the flow field, which is examined on the 2D NACA0015 and 3D NACA0012 blade profile using SST k-ω turbulence model to compute the unsteady flow field. We inserted the time-dependent flow area variables in Ffowcs-Williams and Hawkings (FW-H) equations as an input and Sound Pressure Level (SPL) values will be computed for different angles of attack (AoA) from the microphone which is positioned in the computational domain to investigate effect of augmentation of unsteady 2D and 3D airfoil region noise level. The computed results will be compared with experimental data which are available in the open literature. As results; one of the calculated Cp is slightly lower than the experimental value. This difference could be due to the higher Reynolds number of the experimental data. The ANSYS Fluent software was used in this study. Fluent includes well-validated physical modeling capabilities to deliver fast, accurate results across the widest range of CFD and multiphysics applications. This paper includes a study which is on external flow over an airfoil. The case of 2D NACA0015 has approximately 7 million elements and solves compressible fluid flow with heat transfer using the SST turbulence model. The other case of 3D NACA0012 has approximately 3 million elements.

Keywords: Aeroacoustics, Ffowcs-Williams and Hawkings equations, SST k-ω turbulence model, Noise Disturbance, 3D Blade Profile, 2D Blade Profile.

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Authors: A. Fakhri Makram, Marwa S. Alwazni, Al-Douri Yarub, Evan T. Salim, Hashim Uda, Chin C. Woei

Abstract:

Lithium niobate (LiNbO₃) nanostructures are prepared on quartz substrate by the sol-gel method. They have been deposited with different molarity concentration and annealed at 500°C. These samples are characterized and analyzed by X-ray diffraction (XRD), Scanning Electron Microscope (SEM) and Atomic Force Microscopy (AFM). The measured results showed an importance increasing in molarity concentrations that indicate the structure starts to become crystal, regular, homogeneous, well crystal distributed, which made it more suitable for optical waveguide application.

Keywords: Lithium niobate, morphological properties, Pechini method, thin film.

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Authors: Adla Bentellis, Zizette Boufaïda

Abstract:

Nowadays, the pace of business change is such that, increasingly, new functionality has to be realized and reliably installed in a matter of days, or even hours. Consequently, more and more business processes are prone to a continuous change. The objective of the research in progress is to use the MAP model, in a conceptual modeling method for flexible and adaptive business process. This method can be used to capture the flexibility dimensions of a business process; it takes inspiration from modularity concept in the object oriented paradigm to establish a hierarchical construction of the BP modeling. Its intent is to provide a flexible modeling that allows companies to quickly adapt their business processes.

Keywords: Business Process, Business process modeling, flexibility, MAP Model.

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Authors: Miquel Colobran, Josep M. Basart

Abstract:

One of the most ancient humankind concerns is knowledge formalization i.e. what a concept is. Concept Analysis, a branch of analytical philosophy, relies on the purpose of decompose the elements, relations and meanings of a concept. This paper aims at presenting a method to make a concept analysis obtaining a knowledge representation suitable to be processed by a computer system using either object-oriented or ontology technologies. Security notion is, usually, known as a set of different concepts related to “some kind of protection". Our method concludes that a more general framework for the concept, despite it is dynamic, is possible and any particular definition (instantiation) depends on the elements used by its construction instead of the concept itself.

Keywords: Concept analysis, Knowledge representation, Security, UML.

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Authors: Vlado Kitanovski, Dimitar Taskovski, Sofija Bogdanova

Abstract:

In this paper we present a combined hashing/watermarking method for image authentication. A robust image hash, invariant to legitimate modifications, but fragile to illegitimate modifications is generated from the local image characteristics. To increase security of the system the watermark is generated using the image hash as a key. Quantized Index Modulation of DCT coefficients is used for watermark embedding. Watermark detection is performed without use of the original image. Experimental results demonstrate the effectiveness of the presented method in terms of robustness and fragility.

Keywords: authentication, blind watermarking, image hash, semi-fragile watermarking

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Authors: G. Kehl, P. Wagner

Abstract:

A novel simulation method to determine the displacements of machine tools due to thermal factors is presented. The specific characteristic of this method is the employment of original CAD data from the design process chain, which is interpreted by an algorithm in terms of geometry-based allocation of convection and radiation parameters. Furthermore analogous models relating to the thermal behaviour of machine elements are automatically implemented, which were gained by extensive experimental testing with thermography imaging. With this a transient simulation of the thermal field and in series of the displacement of the machine tool is possible simultaneously during the design phase. This method was implemented and is already used industrially in the design of machining centres in order to improve the quality of herewith manufactured workpieces.

Keywords: Accuracy, design process, finite element analysis, machine tools, thermal simulation.

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Authors: Mohammad R. Jalali, Mohammad M. Jalali

Abstract:

The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.

Keywords: Even harmonic components of sloshing waves, Green–Naghdi equations, nonlinearity, solitary waves.

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Authors: Naima Ikken, Abdelhadi Bouknadel, Nour-eddine Tariba Ahmed Haddou, Hafsa El Omari

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The operation of grid-connected inverters necessity a single-phase phase locked loop (PLL) is proposed in this article to accurately and quickly estimate and detect the grid phase angle. This article presents the improvement of a method of phase-locked loop. The novelty is to generate a method (PLL) of synchronizing the grid with a Notch filter based on adaptive fuzzy logic for inverter systems connected to the grid. The performance of the proposed method was tested under normal and abnormal operating conditions (amplitude, frequency and phase shift variations). In addition, simulation results with ISPM software are developed to verify the effectiveness of the proposed method strategy. Finally, the experimental test will be used to extract the result and discuss the validity of the proposed algorithm.

Keywords: Phase locked loop, PLL, notch filter, fuzzy logic control.

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Authors: Foad Nazari, Seyed Mahmood Hosseini, Mohammad Hossein Abolbashari, Mohammad Hassan Abolbashari

Abstract:

The present study is concerned with the optimal design of functionally graded plates using particle swarm optimization (PSO) algorithm. In this study, meshless local Petrov-Galerkin (MLPG) method is employed to obtain the functionally graded (FG) plate’s natural frequencies. Effects of two parameters including thickness to height ratio and volume fraction index on the natural frequencies and total mass of plate are studied by using the MLPG results. Then the first natural frequency of the plate, for different conditions where MLPG data are not available, is predicted by an artificial neural network (ANN) approach which is trained by back-error propagation (BEP) technique. The ANN results show that the predicted data are in good agreement with the actual one. To maximize the first natural frequency and minimize the mass of FG plate simultaneously, the weighted sum optimization approach and PSO algorithm are used. However, the proposed optimization process of this study can provide the designers of FG plates with useful data.

Keywords: Optimal design, natural frequency, FG plate, hybrid meshless method, MLPG method, ANN approach, particle swarm optimization.

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Authors: Weifeng Wang, Hengbin Zheng, Xianwei Zeng

Abstract:

The launching nose plays an important role in the incremental launching construction. The parameters of the launching nose essentially affect the internal forces of the girder during the construction. The appropriate parameters can decrease the internal forces in the girder and save the material and reduce the cost. The simplified structural model, which is made with displacement method according to the characteristic of incremental launching construction and the variation rule of the internal forces, calculates and analyzes the effect of the length, the rigidity and weight of launch nose on the internal forces of girder during the incremental launching construction. The method, which can calculate the launching nose parameters for the optimum incremental launching construction, is achieved. This method is simple, reliable and easy for practical use.

Keywords: incremental launching, launching nose, optimumanalysis, displacement method

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Authors: Yuka Kawakami, Tomoyuki Yokogawa, Hisashi Miyazaki, Sousuke Amasaki, Yoichiro Sato, Michiyoshi Hayase

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In this paper, we proposed a method for detecting consistency violation between state machine diagrams and a sequence diagram defined in UML 2.0 using SMV. We extended a method expressing these diagrams defined in UML 1.0 with boolean formulas so that it can express a sequence diagram with combined fragments introduced in UML 2.0. This extension made it possible to represent three types of combined fragment: alternative, option and parallel. As a result of experiment, we confirmed that the proposed method could detect consistency violation correctly with SMV.

Keywords: UML, model checking, SMV, sequence diagram.

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Authors: Tianchai Suksri, U-thai Sritheeravirojana, Arjin Numsomran, Viriya Kongrattana, Thongchai Werataweemart

Abstract:

A control system design with Characteristic Ratio Assignment (CRA) is proven that effective for SISO control design. But the control system design for MIMO via CRA is not concrete procedure. In this paper presents the control system design method for quadruple-tank process via CRA. By using the decentralized method for both minimum phase and non-minimum phase are made. The results from PI and PID controller design via CRA can be illustrated the validity of our approach by MATLAB.

Keywords: CRA, Quadruple-Tank.

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Authors: E. Aruchunan, J. Sulaiman

Abstract:

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half- Sweep Gauss-Seidel (HSGS) methods are also presented. The HSGS method has been shown to rapid compared to the FSGS methods. Some numerical tests were illustrated to show that the HSGS method is superior to the FSGS method.

Keywords: Integro-differential equations, Linear fredholm equations, Finite difference, Quadrature formulas, Half-Sweep iteration.

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Authors: Yong-jun Zhao, Heng-li Zhang, Zong-yun Hu

Abstract:

Based on the sources- smoothed rank profile (SRP) and modified minimum description length (MMDL) principle, a method for estimation of the source coherency structure (SCS) and the number of wideband sources is proposed in this paper. Instead of focusing, we first use a spatial smoothing technique to pre-process the array covariance matrix of each frequency for de-correlating the sources and then use smoothed rank profile to determine the SCS and the number of wideband sources. We demonstrate the availability of the method by numerical simulations.

Keywords: Wideband sources, source coherency structure (SCS), smoothed rank profile (SRP).

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Authors: H. Alaleh, N. Hedayat, A. Alaleh, H. Ayazi, A. Ruhani

Abstract:

Run-offs are considered as important hydrological factors in feasibility studies of river engineering and irrigation-related projects under arid and semi-arid condition. Flood control is one of the crucial factor, the management of which while mitigates its destructive consequences, abstracts considerable volume of renewable water resources. The methodology applied here was based on Mizumura, which applied a mathematical model for simple tank to simulate the rainfall-run-off process in a particular water basin using the data from the observational hydrograph. The model was applied in the Dez River water basin adjacent to Greater Dezful region, Iran in order to simulate and estimate the floods. Results indicated that the calculated hydrographs using the simple tank method, SCS-CN model and the observation hydrographs had a close proximity. It was also found that on average the flood time and discharge peaks in the simple tank were closer to the observational data than the CN method. On the other hand, the calculated flood volume in the CN model was significantly closer to the observational data than the simple tank model.

Keywords: Simple tank, Dez River, run-off, lag time, excess rainfall.

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Authors: Said M. Easa, Shinya Kikuchi

Abstract:

When the profile information of an existing road is missing or not up-to-date and the parameters of the vertical alignment are needed for engineering analysis, the engineer has to recreate the geometric design features of the road alignment using collected profile data. The profile data may be collected using traditional surveying methods, global positioning systems, or digital imagery. This paper develops a method that estimates the parameters of the geometric features that best characterize the existing vertical alignments in terms of tangents and the expressions of the curve, that may be symmetrical, asymmetrical, reverse, and complex vertical curves. The method is implemented using an Excel-based optimization method that minimizes the differences between the observed profile and the profiles estimated from the equations of the vertical curve. The method uses a 'wireframe' representation of the profile that makes the proposed method applicable to all types of vertical curves. A secondary contribution of this paper is to introduce the properties of the equal-arc asymmetrical curve that has been recently developed in the highway geometric design field.

Keywords: Optimization, parameters, data, reverse, spreadsheet, vertical curves

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Authors: N. Z. A. Hamid, M. S. M. Noorani

Abstract:

This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly Ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: Chaotic approach, phase space, Cao method, local linear approximation method.

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Authors: O. Rahli, N. Mimouni, R. Bennacer, K. Bouhadef

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This numerical study investigates the travelling wave’s appearance and the behavior of Poiseuille-Rayleigh-Benard (PRB) flow induced in 3D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The governing equations are discretized by using a control volume method with third order Quick scheme in approximating the advection terms. Simpler algorithm is used to handle coupling between the momentum and continuity equations. To avoid the excessively high computer time, full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For a broad range of dimensionless controlling parameters, the contribution of this work is to analyzing the flow regimes of the steady longitudinal thermoconvective rolls (noted R//) for both thermal and mass transfer (TSMC). The transition from the opposed volume forces to cooperating ones, considerably affects the birth and the development of the longitudinal rolls. The heat and mass transfers distribution are also examined.

Keywords: Heat and mass transfer, mixed convection, Poiseuille-Rayleigh-Benard flow, rectangular duct.

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Authors: Ali Reza Sahab, Amir Gholami Pastaki

Abstract:

In this paper, backstepping method (BM) is proposed for a single-link flexible mechanical manipulator. In each step of this method a positive value is obtained. Selections of the gain factor values are very important because controller will have different behavior for each different set of values. Improper selection of these gains can lead to instability of the system. In order to choose proper values for gains BELBIC method has been used in this work. Finally, to prove the efficiency of this method, the obtained results of proposed model are compared with robust controller one. Results show that the combination of backstepping and BELBIC that is presented here, can stabilized the system with higher speed, shorter settling time and lower overshoot in than robust controller.

Keywords: single-link flexible manipulator, backstepping, BELBIC

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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: Süha Yılmaz, Melih Turgut

Abstract:

These In this work, a regular unit speed curve in six dimensional Euclidean space, whose Frenet curvatures are constant, is considered. Thereafter, a method to calculate Frenet apparatus of this curve is presented.

Keywords: Classical Differential Geometry, Euclidean 6-space, Frenet Apparatus of the curves.

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Authors: Talib Hashim Hasan

Abstract:

This paper describes simple implementation of homotopy (also called continuation) algorithm for determining the proper resistance of the resistor to dissipate energy at a specified rate of an electric circuit. Homotopy algorithm can be considered as a developing of the classical methods in numerical computing such as Newton-Raphson and fixed point methods. In homoptopy methods, an embedding parameter is used to control the convergence. The method purposed in this work utilizes a special homotopy called Newton homotopy. Numerical example solved in MATLAB is given to show the effectiveness of the purposed method

Keywords: electrical circuit homotopy, methods, MATLAB, Newton homotopy

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Authors: Deyu Sun, Guangbin Wang

Abstract:

In this paper, we present preconditioned generalized accelerated overrelaxation (GAOR) methods for solving certain nonsingular linear system. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give two numerical examples to confirm our theoretical results.

Keywords: Preconditioned, GAOR method, linear system, convergence, comparison.

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