Search results for: Optimal linear quadratic tracker

Authors: YuriyTasinkevych, Ihor Trots, AndrzejNowicki, Marcin Lewandowski

Abstract:

The paper presents the optimization problem for the multi-element synthetic transmit aperture method (MSTA) in ultrasound imaging applications. The optimal choice of the transmit aperture size is performed as a trade-off between the lateral resolution, penetration depth and the frame rate. Results of the analysis obtained by a developed optimization algorithm are presented. Maximum penetration depth and the best lateral resolution at given depths are chosen as the optimization criteria. The optimization algorithm was tested using synthetic aperture data of point reflectors simulated by Filed II program for Matlab® for the case of 5MHz 128-element linear transducer array with 0.48 mm pitch are presented. The visualization of experimentally obtained synthetic aperture data of a tissue mimicking phantom and in vitro measurements of the beef liver are also shown. The data were obtained using the SonixTOUCH Research systemequipped with a linear 4MHz 128 element transducerwith 0.3 mm element pitch, 0.28 mm element width and 70% fractional bandwidth was excited by one sine cycle pulse burst of transducer's center frequency.

Keywords: synthetic aperture method, ultrasound imaging, beamforming.

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Authors: I. A. Farhat

Abstract:

The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand.  Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: Artificial Immune System (AIS), Dynamic Economic Dispatch (DED).

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Authors: A. Ourici

Abstract:

Doubly fed induction machines DFIM are used mainly for wind energy conversion in MW power plants. This paper presents a new strategy of field oriented control ,it is based on the principle of a double flux orientation of stator and rotor at the same time. Therefore, the orthogonality created between the two oriented fluxes, which must be strictly observed, leads to generate a linear and decoupled control with an optimal torque. The obtained simulation results show the feasibility and the effectiveness of the suggested method.

Keywords: Doubly fed induction machine, double fluxorientation control , vector control , PWM inverter.

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Authors: A. M. Sagir

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In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Tsai-Sheng Kao

Abstract:

The ideal sinc filter, ignoring the noise statistics, is often applied for generating an arbitrary sample of a bandlimited signal by using the uniformly sampled data. In this article, an optimal interpolator is proposed; it reaches a minimum mean square error (MMSE) at its output in the presence of noise. The resulting interpolator is thus a Wiener filter, and both the optimal infinite impulse response (IIR) and finite impulse response (FIR) filters are presented. The mean square errors (MSE-s) for the interpolator of different length impulse responses are obtained by computer simulations; it shows that the MSE-s of the proposed interpolators with a reasonable length are improved about 0.4 dB under flat power spectra in noisy environment with signal-to-noise power ratio (SNR) equal 10 dB. As expected, the results also demonstrate the improvements for the MSE-s with various fractional delays of the optimal interpolator against the ideal sinc filter under a fixed length impulse response.

Keywords: Interpolator, minimum mean square error, Wiener filter.

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Authors: Chao Yi, Cunyue Lu, Lingwei Quan

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Piezoelectric linear motors have the characteristics of great electromagnetic compatibility, high positioning accuracy, compact structure and no deceleration mechanism, which make it promising to applicate in micro-miniature precision drive systems. However, most piezoelectric motors are employed by flexible clamping, which has insufficient rigidity and is difficult to use in rapid positioning. Another problem is that this clamping method seriously affects the vibration efficiency of the vibrating unit. In order to solve these problems, this paper proposes a piezoelectric stack linear motor based on double-end rigid clamping. First, a piezoelectric linear motor with a length of only 35.5 mm is designed. This motor is mainly composed of a motor stator, a driving foot, a ceramic friction strip, a linear guide, a pre-tightening mechanism and a base. This structure is much simpler and smaller than most similar motors, and it is easy to assemble as well as to realize precise control. In addition, the properties of piezoelectric stack are reviewed and in order to obtain the elliptic motion trajectory of the driving head, a driving scheme of the longitudinal-shear composite stack is innovatively proposed. Finally, impedance analysis and speed performance testing were performed on the piezoelectric linear motor prototype. The motor can measure speed up to 25.5 mm/s under the excitation of signal voltage of 120 V and frequency of 390 Hz. The result shows that the proposed piezoelectric stacked linear motor obtains great performance. It can run smoothly in a large speed range, which is suitable for various precision control in medical images, aerospace, precision machinery and many other fields.

Keywords: Elliptical trajectory, linear motor, piezoelectric stack, rigid clamping.

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Authors: H. Shayeghi, H. Hosseini, A. Shabani, M. Mahdavi

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In this paper, optimal generation expansion planning (GEP) is investigated considering purchase prices, profits of independent power producers (IPPs) and reliability criteria using a new method based on hybrid coded Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). In this approach, optimal purchase price of each IPP is obtained by HCGA and reliability criteria are calculated by PSO technique. It should be noted that reliability criteria and the rate of carbon dioxide (CO2) emission have been considered as constraints of the GEP problem. Finally, the proposed method has been tested on the case study system. The results evaluation show that the proposed method can simply obtain optimal purchase prices of IPPs and is a fast method for calculation of reliability criteria in expansion planning. Also, considering the optimal purchase prices and profits of IPPs in generation expansion planning are caused that the expansion costs are decreased and the problem is solved more exactly.

Keywords: GEP Problem, IPPs, Reliability Criteria, GA, PSO.

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Authors: Chan-Sik Kim, Jong-Seong Kim, Se Won Lee, Hoo-Gon Choi

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In rapidly changing market environment, firms are investing a lot of time and resources into new product development (NPD) projects to make profit and to obtain competitive advantage. However, failure rate of NPD projects is becoming high due to various internal and external risks which hinder successful NPD projects. To reduce the failure rate, it is critical that risks have to be managed effectively and efficiently through good strategy, and treated by optimal responses to minimize risk cost. Four strategies are adopted to handle the risks in this study. The optimal responses are characterized by high reduction of risk costs with high efficiency. This study suggests a framework to decide the optimal responses considering the core risks, risk costs, response efficiency and response costs for successful NPD projects. Both binary particles warm optimization (BPSO) and multi-objective particle swarm optimization (MOPSO) methods are mainly used in the framework. Although several limitations exist in use for real industries, the frame work shows good strength for handling the risks with highly scientific ways through an example.

Keywords: NPD projects, risk cost, strategy, optimal responses, Particle Swarm Optimization.

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Authors: R.Muthuvelayudham, T.Viruthagiri

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Response Surface Methodology (RSM) is a powerful and efficient mathematical approach widely applied in the optimization of cultivation process. Cellulase enzyme production by Trichoderma reesei RutC30 using agricultural waste rice straw and banana fiber as carbon source were investigated. In this work, sequential optimization strategy based statistical design was employed to enhance the production of cellulase enzyme through submerged cultivation. A fractional factorial design (26-2) was applied to elucidate the process parameters that significantly affect cellulase production. Temperature, Substrate concentration, Inducer concentration, pH, inoculum age and agitation speed were identified as important process parameters effecting cellulase enzyme synthesis. The concentration of lignocelluloses and lactose (inducer) in the cultivation medium were found to be most significant factors. The steepest ascent method was used to locate the optimal domain and a Central Composite Design (CCD) was used to estimate the quadratic response surface from which the factor levels for maximum production of cellulase were determined.

Keywords: Banana fiber, Cellulase, Optimization, Rice straw

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Authors: Rafael Jorge Menezes Santos, Ginalber Luiz de Oliveira Serra, Carlos César Teixeira Ferreira

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This paper proposes a methodology for analysis of the dynamic behavior of a robotic manipulator in continuous time. Initially this system (nonlinear system) will be decomposed into linear submodels and analyzed in the context of the Linear and Parameter Varying (LPV) Systems. The obtained linear submodels, which represent the local dynamic behavior of the robotic manipulator in some operating points were grouped in a Takagi-Sugeno fuzzy structure. The obtained fuzzy model was analyzed and validated through analog simulation, as universal approximator of the robotic manipulator.

Keywords: modeling of nonlinear dynamic systems, Takagi- Sugeno fuzzy model, Linear and Parameter Varying (LPV) System.

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Authors: Fatemeh Amiri, Caro Lucas, Nasser Yazdani

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As the network based technologies become omnipresent, demands to secure networks/systems against threat increase. One of the effective ways to achieve higher security is through the use of intrusion detection systems (IDS), which are a software tool to detect anomalous in the computer or network. In this paper, an IDS has been developed using an improved machine learning based algorithm, Locally Linear Neuro Fuzzy Model (LLNF) for classification whereas this model is originally used for system identification. A key technical challenge in IDS and LLNF learning is the curse of high dimensionality. Therefore a feature selection phase is proposed which is applicable to any IDS. While investigating the use of three feature selection algorithms, in this model, it is shown that adding feature selection phase reduces computational complexity of our model. Feature selection algorithms require the use of a feature goodness measure. The use of both a linear and a non-linear measure - linear correlation coefficient and mutual information- is investigated respectively

Keywords: anomaly Detection, feature selection, Locally Linear Neuro Fuzzy (LLNF), Mutual Information (MI), liner correlation coefficient.

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Authors: M. Esmaeeli Shahrakht, A. Kazemi

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Due to uncertainty of wind velocity, wind power generators don’t have deterministic output power. Utilizing wind power generation and thermal power plants together create new concerns for operation engineers of power systems. In this paper, a model is presented to implement the uncertainty of load and generated wind power which can be utilized in power system operation planning. Stochastic behavior of parameters is simulated by generating scenarios that can be solved by deterministic method. A mixed-integer linear programming method is used for solving deterministic generation scheduling problem. The proposed approach is applied to a 12-unit test system including 10 thermal units and 2 wind farms. The results show affectivity of piecewise linear model in unit commitment problems. Also using linear programming causes a considerable reduction in calculation times and guarantees convergence to the global optimum. Neglecting the uncertainty of wind velocity causes higher cost assessment of generation scheduling.

Keywords: Load uncertainty, linear programming, scenario generation, unit commitment, wind farm.

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Authors: A. Safari, R. Jahani, H. A. Shayanfar, J. Olamaei

Abstract:

This paper shows the results obtained in the analysis of the impact of distributed generation (DG) on distribution losses and presents a new algorithm to the optimal allocation of distributed generation resources in distribution networks. The optimization is based on a Hybrid Genetic Algorithm and Particle Swarm Optimization (HGAPSO) aiming to optimal DG allocation in distribution network. Through this algorithm a significant improvement in the optimization goal is achieved. With a numerical example the superiority of the proposed algorithm is demonstrated in comparison with the simple genetic algorithm.

Keywords: Distributed Generation, Distribution Networks, Genetic Algorithm, Particle Swarm Optimization.

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Authors: S. Raja Balachandar, K.Kannan

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This paper presents a heuristic approach to solve the Generalized Assignment Problem (GAP) which is NP-hard. It is worth mentioning that many researches used to develop algorithms for identifying the redundant constraints and variables in linear programming model. Some of the algorithms are presented using intercept matrix of the constraints to identify redundant constraints and variables prior to the start of the solution process. Here a new heuristic approach based on the dominance property of the intercept matrix to find optimal or near optimal solution of the GAP is proposed. In this heuristic, redundant variables of the GAP are identified by applying the dominance property of the intercept matrix repeatedly. This heuristic approach is tested for 90 benchmark problems of sizes upto 4000, taken from OR-library and the results are compared with optimum solutions. Computational complexity is proved to be O(mn2) of solving GAP using this approach. The performance of our heuristic is compared with the best state-ofthe- art heuristic algorithms with respect to both the quality of the solutions. The encouraging results especially for relatively large size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems.

Keywords: Combinatorial Optimization Problem, Generalized Assignment Problem, Intercept Matrix, Heuristic, Computational Complexity, NP-Hard Problems.

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Authors: Loredana G. Marcu, David Marcu, Sanda M. Filip

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Advanced head and neck cancers are aggressive tumours, which require aggressive treatment. Treatment efficiency is often hindered by cancer cell repopulation during radiotherapy, which is due to various mechanisms triggered by the loss of tumour cells and involves both stem and differentiated cells. The aim of the current paper is to present in silico simulations of radiotherapy schedules on a virtual head and neck tumour grown with biologically realistic kinetic parameters. Using the linear quadratic formalism of cell survival after radiotherapy, altered fractionation schedules employing various treatment breaks for normal tissue recovery are simulated and repopulation mechanism implemented in order to evaluate the impact of various cancer cell contribution on tumour behaviour during irradiation. The model has shown that the timing of treatment breaks is an important factor influencing tumour control in rapidly proliferating tissues such as squamous cell carcinomas of the head and neck. Furthermore, not only stem cells but also differentiated cells, via the mechanism of abortive division, can contribute to malignant cell repopulation during treatment.

Keywords: Radiation, tumour repopulation, squamous cell carcinoma, stem cell.

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Authors: Inta Volodko, Valentina Koliskina

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Linear stability of wake-shear layers in two-phase shallow flows is analyzed in the present paper. Stability analysis is based on two-dimensional shallow water equations. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. Linear stability curves are obtained for different values of the particle loading parameter, the velocity ratio and the velocity deficit. It is shown that the increase in the velocity ratio destabilizes the flow. The particle loading parameter has a stabilizing effect on the flow. The role of the velocity deficit is also destabilizing: the increase of the velocity deficit leads to less stable flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: T. Balogh, L. G. Vigh

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Seismic design may require non-conventional concept, due to the fact that the stiffness and layout of the structure have a great effect on the overall structural behaviour, on the seismic load intensity as well as on the internal force distribution. To find an economical and optimal structural configuration the key issue is the optimal design of the lateral load resisting system. This paper focuses on the optimal design of regular, concentric braced frame (CBF) multi-storey steel building structures. The optimal configurations are determined by a numerical method using genetic algorithm approach, developed by the authors. Aim is to find structural configurations with minimum structural cost. The design constraints of objective function are assigned in accordance with Eurocode 3 and Eurocode 8 guidelines. In this paper the results are presented for various building geometries, different seismic intensities, and levels of energy dissipation.

Keywords: Dissipative Structures, Genetic Algorithm, Seismic Effects, Structural Optimization.

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Authors: Gabriel Sitler, Yousef Sardahi, Asad Salem

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This paper presents an optimal and robust sliding mode controller (SMC) to regulate the position of the knee joint angle for patients suffering from knee injuries. The controller imitates the role of active orthoses that produce the joint torques required to overcome gravity and loading forces and regain natural human movements. To this end, a mathematical model of the shank, the lower part of the leg, is derived first and then used for the control system design and computer simulations. The design of the controller is carried out in optimal and multi-objective settings. Four objectives are considered: minimization of the control effort and tracking error; and maximization of the control signal smoothness and closed-loop system’s speed of response. Optimal solutions in terms of the Pareto set and its image, the Pareto front, are obtained. The results show that there are trade-offs among the design objectives and many optimal solutions from which the decision-maker can choose to implement. Also, computer simulations conducted at different points from the Pareto set and assuming knee squat movement demonstrate competing relationships among the design goals. In addition, the proposed control algorithm shows robustness in tracking a standard gait signal when accounting for uncertainty in the shank’s parameters.

Keywords: Optimal control, multi-objective optimization, sliding mode control, wearable knee exoskeletons.

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Authors: Satoshi Usami

Abstract:

Among various HLM techniques, the Multivariate Hierarchical Linear Model (MHLM) is desirable to use, particularly when multivariate criterion variables are collected and the covariance structure has information valuable for data analysis. In order to reflect prior information or to obtain stable results when the sample size and the number of groups are not sufficiently large, the Bayes method has often been employed in hierarchical data analysis. In these cases, although the Markov Chain Monte Carlo (MCMC) method is a rather powerful tool for parameter estimation, Procedures regarding MCMC have not been formulated for MHLM. For this reason, this research presents concrete procedures for parameter estimation through the use of the Gibbs samplers. Lastly, several future topics for the use of MCMC approach for HLM is discussed.

Keywords: Gibbs sampler, Hierarchical Linear Model, Markov Chain Monte Carlo, Multivariate Hierarchical Linear Model

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Authors: Changchun Shen, Shouming Zhong

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This paper investigates the robust stability of uncertain neutral system with time-varying delay. By using Lyapunov method and linear matrix inequality technology, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs), which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Neutral system, linear matrix inequalities, Lyapunov, stability.

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Authors: Vultchan T. Gueorgiev, Racho M. Ivanov, Ivan S. Yatchev, Krastyo L. Hinov

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An approach for experimental measurement of the dynamic characteristics of linear electromagnet actuators is presented. It uses accelerometer sensor to register the armature acceleration. The velocity and displacement of the moving parts can be obtained by integration of the acceleration results. The armature movement of permanent magnet linear actuator is acquired using this technique. The results are analyzed and the performance of the supposed approach is compared with the most commonly used experimental setup where the displacement of the armature vs. time is measured instead of its acceleration.

Keywords: Dynamic characteristics, dynamic simulation, linearactuators.

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Authors: Birol Yildiz, Abdullah Yalama, Metin Coskun

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Many studies have shown that Artificial Neural Networks (ANN) have been widely used for forecasting financial markets, because of many financial and economic variables are nonlinear, and an ANN can model flexible linear or non-linear relationship among variables. The purpose of the study was to employ an ANN models to predict the direction of the Istanbul Stock Exchange National 100 Indices (ISE National-100). As a result of this study, the model forecast the direction of the ISE National-100 to an accuracy of 74, 51%.

Keywords: Artificial Neural Networks, Istanbul StockExchange, Non-linear Modeling.

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Authors: George Yungchih Wang

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For decades financial economists have been attempted to determine the optimal investment policy by recognizing the option value embedded in irreversible investment whose project value evolves as a geometric Brownian motion (GBM). This paper aims to examine the effects of the optimal investment trigger and of the misspecification of stochastic processes on investment in real options applications. Specifically, the former explores the consequence of adopting optimal investment rules on the distributions of corporate value under the correct assumption of stochastic process while the latter analyzes the influence on the distributions of corporate value as a result of the misspecification of stochastic processes, i.e., mistaking an alternative process as a GBM. It is found that adopting the correct optimal investment policy may increase corporate value by shifting the value distribution rightward, and the misspecification effect may decrease corporate value by shifting the value distribution leftward. The adoption of the optimal investment trigger has a major impact on investment to such an extent that the downside risk of investment is truncated at the project value of zero, thereby moving the value distributions rightward. The analytical framework is also extended to situations where collection lags are in place, and the result indicates that collection lags reduce the effects of investment trigger and misspecification on investment in an opposite way.

Keywords: GBM, real options, investment trigger, misspecification, collection lags

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Authors: Ejaz Khan, Conor Heneghan

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In this paper we propose a new criterion for solving the problem of channel shortening in multi-carrier systems. In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Minimum mean square error (MMSE) method for TEQ does not give satisfactory results. In [1] a new criterion for partially equalizing severe ISI channels to reduce the cyclic prefix overhead of the discrete multitone transceiver (DMT), assuming a fixed transmission bandwidth, is introduced. Due to specific constrained (unit morm constraint on the target impulse response (TIR)) in their method, the freedom to choose optimum vector (TIR) is reduced. Better results can be obtained by avoiding the unit norm constraint on the target impulse response (TIR). In this paper we change the cost function proposed in [1] to the cost function of determining the maximum of a determinant subject to linear matrix inequality (LMI) and quadratic constraint and solve the resulting optimization problem. Usefulness of the proposed method is shown with the help of simulations.

Keywords: Equalizer, target impulse response, convex optimization, matrix inequality.

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Authors: Ryosuke Ito, Goro Obinata, Chikara Nagai, Youngwoo Kim

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This paper proposes a new parameter identification method based on Linear Fractional Transformation (LFT). It is assumed that the target linear system includes unknown parameters. The parameter deviations are separated from a nominal system via LFT, and identified by organizing I/O signals around the separated deviations of the real system. The purpose of this paper is to apply LFT to simultaneously identify the parameter deviations in systems with fewer outputs than unknown parameters. As a fundamental example, this method is implemented to one degree of freedom vibratory system. Via LFT, all physical parameters were simultaneously identified in this system. Then, numerical simulations were conducted for this system to verify the results. This study shows that all the physical parameters of a system with fewer outputs than unknown parameters can be effectively identified simultaneously using LFT.

Keywords: Identification, Linear Fractional Transformation, Right inverse system

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Authors: V. Tawiwat, T. Amornthep, P. Pnop

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Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper considers the indirect minimum Jerk method for higher order differential equation in dynamics optimization proposes a simple yet very interesting indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of indirect jerks are found using the dynamic optimization methods together with the numerical approximation. This case considers the linear equation of a simple system, for instance, mass, spring and damping. The simple system uses two mass connected together by springs. The boundary initial is defined the fix end time and end point. The higher differential order is solved by Galerkin-s methods weight residual. As the result, the 6th higher differential order shows the faster solving time.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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Authors: Sang Wook Park, Se Woon Choi, Yousok Kim, Byung Kwan Oh, Hyo Seon Park

Abstract:

Various retrofit techniques for reinforced concrete frame with infill wall have been steadily developed. Among those techniques, strengthening methodology based on diagonal FRP strips (FRP bracings) has numerous advantages such as feasibility of implementing without interrupting the building under operation, reduction of cost and time, and easy application. Considering the safety of structure and retrofit cost, the most appropriate retrofit solution is needed. Thus, the objective of this study is to suggest pareto-optimal solution for existing building using FRP bracings. To find pareto-optimal solution analysis, NSGA-II is applied. Moreover, the seismic performance of retrofit building is evaluated. The example building is 5-storey, 3-bay RC frames with infill wall. Nonlinear static pushover analyses are performed with FEMA 356. The criterion of performance evaluation is inter-story drift ratio at the performance level IO, LS, CP. Optimal retrofit solutions is obtained for 32 individuals and 200 generations. Through the proposed optimal solutions, we confirm the improvement of seismic performance of the example building.

Keywords: Retrofit, FRP bracings, reinforced concrete frame with infill wall, seismic performance evaluation, NSGA-II.

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Authors: Mei Li, Fahui Zhai

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In this paper, the definitions of the quaternion measure and the quaternion vector measure are introduced. The relation between the quaternion measure and the complex vector measure as well as the relation between the quaternion linear functional and the complex linear functional are discussed respectively. By using these relations, the necessary and sufficient condition to determine the quaternion vector measure is given.

Keywords: Quaternion, Quaternion measure, Quaternion vector measure, Quaternion Banach space, Quaternion linear functional.

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Authors: Adil AL-Rammahi

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In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.

Keywords: Fredholm integral equation, power series, Banach fixed point theorem, Linear Systems.

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Authors: Deyu Sun, Guangbin Wang

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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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