Search results for: linear least squares.
1792 Jacobi-Based Methods in Solving Fuzzy Linear Systems
Authors: Lazim Abdullah, Nurhakimah Ab. Rahman
Abstract:
Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.
Keywords: Fuzzy linear systems, Jacobi, Jacobi Over- Relaxation, Refinement of Jacobi, Refinement of Jacobi Over- Relaxation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23721791 Block Homotopy Perturbation Method for Solving Fuzzy Linear Systems
Authors: Shu-Xin Miao
Abstract:
In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.
Keywords: Homotopy perturbation method, fuzzy linear systems, block linear system, fuzzy solution, embedding parameter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13191790 Model Predictive Fuzzy Control of Air-ratio for Automotive Engines
Authors: Hang-cheong Wong, Pak-kin Wong, Chi-man Vong, Zhengchao Xie, Shaojia Huang
Abstract:
Automotive engine air-ratio plays an important role of emissions and fuel consumption reduction while maintains satisfactory engine power among all of the engine control variables. In order to effectively control the air-ratio, this paper presents a model predictive fuzzy control algorithm based on online least-squares support vector machines prediction model and fuzzy logic optimizer. The proposed control algorithm was also implemented on a real car for testing and the results are highly satisfactory. Experimental results show that the proposed control algorithm can regulate the engine air-ratio to the stoichiometric value, 1.0, under external disturbance with less than 5% tolerance.Keywords: Air-ratio, Fuzzy logic, online least-squares support vector machine, model predictive control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17681789 Equity Risk Premiums and Risk Free Rates in Modelling and Prediction of Financial Markets
Authors: Mohammad Ghavami, Reza S. Dilmaghani
Abstract:
This paper presents an adaptive framework for modelling financial markets using equity risk premiums, risk free rates and volatilities. The recorded economic factors are initially used to train four adaptive filters for a certain limited period of time in the past. Once the systems are trained, the adjusted coefficients are used for modelling and prediction of an important financial market index. Two different approaches based on least mean squares (LMS) and recursive least squares (RLS) algorithms are investigated. Performance analysis of each method in terms of the mean squared error (MSE) is presented and the results are discussed. Computer simulations carried out using recorded data show MSEs of 4% and 3.4% for the next month prediction using LMS and RLS adaptive algorithms, respectively. In terms of twelve months prediction, RLS method shows a better tendency estimation compared to the LMS algorithm.Keywords: Prediction of financial markets, Adaptive methods, MSE, LSE.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9751788 An Iterative Method for Quaternionic Linear Equations
Authors: Bin Yu, Minghui Wang, Juntao Zhang
Abstract:
By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.
Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17201787 Validity Domains of Beams Behavioural Models: Efficiency and Reduction with Artificial Neural Networks
Authors: Keny Ordaz-Hernandez, Xavier Fischer, Fouad Bennis
Abstract:
In a particular case of behavioural model reduction by ANNs, a validity domain shortening has been found. In mechanics, as in other domains, the notion of validity domain allows the engineer to choose a valid model for a particular analysis or simulation. In the study of mechanical behaviour for a cantilever beam (using linear and non-linear models), Multi-Layer Perceptron (MLP) Backpropagation (BP) networks have been applied as model reduction technique. This reduced model is constructed to be more efficient than the non-reduced model. Within a less extended domain, the ANN reduced model estimates correctly the non-linear response, with a lower computational cost. It has been found that the neural network model is not able to approximate the linear behaviour while it does approximate the non-linear behaviour very well. The details of the case are provided with an example of the cantilever beam behaviour modelling.
Keywords: artificial neural network, validity domain, cantileverbeam, non-linear behaviour, model reduction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13871786 A Method for Quality Inspection of Motors by Detecting Abnormal Sound
Authors: Tadatsugu Kitamoto
Abstract:
Recently, a quality of motors is inspected by human ears. In this paper, I propose two systems using a method of speech recognition for automation of the inspection. The first system is based on a method of linear processing which uses K-means and Nearest Neighbor method, and the second is based on a method of non-linear processing which uses neural networks. I used motor sounds in these systems, and I successfully recognize 86.67% of motor sounds in the linear processing system and 97.78% in the non-linear processing system.Keywords: Acoustical diagnosis, Neural networks, K-means, Short-time Fourier transformation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16561785 Unit Root Tests Based On the Robust Estimator
Authors: Wararit Panichkitkosolkul
Abstract:
The unit root tests based on the robust estimator for the first-order autoregressive process are proposed and compared with the unit root tests based on the ordinary least squares (OLS) estimator. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of Type I error and powers of the unit root tests are estimated via Monte Carlo simulation. Simulation results show that all unit root tests can control the probability of Type I error for all situations. The empirical power of the unit root tests based on the robust estimator are higher than the unit root tests based on the OLS estimator.
Keywords: Autoregressive, Ordinary least squares, Type I error, Power of the test, Monte Carlo simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16951784 Numerical Solving of General Fuzzy Linear Systems by Huang's Method
Authors: S. J. Hosseini Ghoncheh, M. Paripour
Abstract:
In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.
Keywords: Fuzzy number, fuzzy linear systems, Huang's method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12441783 Packing and Covering Radii of Linear Error-Block Codes
Authors: Rabiˆı DARITI, El Mamoun SOUIDI
Abstract:
Linear error-block codes are a natural generalization of linear error correcting codes. The purpose of this paper is to generalize some results on the packing and the covering radii to the error-block case. We study their properties when a code undergoes some specific modifications and combinations with another code. We give a few bounds on the packing and the covering radii of these codes.
Keywords: Linear error-block codes, π-distance, Correction capacity, Packing radius, Covering radius.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21361782 Blood Glucose Measurement and Analysis: Methodology
Authors: I. M. Abd Rahim, H. Abdul Rahim, R. Ghazali
Abstract:
There is numerous non-invasive blood glucose measurement technique developed by researchers, and near infrared (NIR) is the potential technique nowadays. However, there are some disagreements on the optimal wavelength range that is suitable to be used as the reference of the glucose substance in the blood. This paper focuses on the experimental data collection technique and also the analysis method used to analyze the data gained from the experiment. The selection of suitable linear and non-linear model structure is essential in prediction system, as the system developed need to be conceivably accurate.Keywords: Invasive, linear, near-infrared (Nir), non-invasive, non-linear, prediction system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8101781 Modeling and Identification of Hammerstein System by using Triangular Basis Functions
Authors: K. Elleuch, A. Chaari
Abstract:
This paper deals with modeling and parameter identification of nonlinear systems described by Hammerstein model having Piecewise nonlinear characteristics such as Dead-zone nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the triangular basis functions leads to a particular form of Hammerstein model. The approximation by using Triangular basis functions for the description of the static nonlinear block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD) technique has been applied to separate the coupled parameters. The proposed approach has been efficiently tested on academic examples of simulation.Keywords: Identification, Hammerstein model, Piecewisenonlinear characteristic, Dead-zone nonlinearity, Triangular basisfunctions, Singular Values Decomposition
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18751780 Kinetic Study of Gluconic Acid Batch Fermentation by Aspergillus niger
Authors: Akbarningrum Fatmawati, Rudy Agustriyanto, Lindawati
Abstract:
Gluconic acid is one of interesting chemical products in industries such as detergents, leather, photographic, textile, and especially in food and pharmaceutical industries. Fermentation is an advantageous process to produce gluconic acid. Mathematical modeling is important in the design and operation of fermentation process. In fact, kinetic data must be available for modeling. The kinetic parameters of gluconic acid production by Aspergillus niger in batch culture was studied in this research at initial substrate concentration of 150, 200 and 250 g/l. The kinetic models used were logistic equation for growth, Luedeking-Piret equation for gluconic acid formation, and Luedeking-Piret-like equation for glucose consumption. The Kinetic parameters in the model were obtained by minimizing non linear least squares curve fitting.Keywords: Aspergillus niger, fermentation, gluconic acid, kinetic.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26481779 Estimating Regression Parameters in Linear Regression Model with a Censored Response Variable
Authors: Jesus Orbe, Vicente Nunez-Anton
Abstract:
In this work we study the effect of several covariates X on a censored response variable T with unknown probability distribution. In this context, most of the studies in the literature can be located in two possible general classes of regression models: models that study the effect the covariates have on the hazard function; and models that study the effect the covariates have on the censored response variable. Proposals in this paper are in the second class of models and, more specifically, on least squares based model approach. Thus, using the bootstrap estimate of the bias, we try to improve the estimation of the regression parameters by reducing their bias, for small sample sizes. Simulation results presented in the paper show that, for reasonable sample sizes and censoring levels, the bias is always smaller for the new proposals.
Keywords: Censored response variable, regression, bias.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14281778 On-line Identification of Continuous-time Hammerstein Systems via RBF Networks and Immune Algorithm
Authors: Tomohiro Hachino, Kengo Nagatomo, Hitoshi Takata
Abstract:
This paper deals with an on-line identification method of continuous-time Hammerstein systems by using the radial basis function (RBF) networks and immune algorithm (IA). An unknown nonlinear static part to be estimated is approximately represented by the RBF network. The IA is efficiently combined with the recursive least-squares (RLS) method. The objective function for the identification is regarded as the antigen. The candidates of the RBF parameters such as the centers and widths are coded into binary bit strings as the antibodies and searched by the IA. On the other hand, the candidates of both the weighting parameters of the RBF network and the system parameters of the linear dynamic part are updated by the RLS method. Simulation results are shown to illustrate the proposed method.Keywords: Continuous-time System, Hammerstein System, OnlineIdentification, Immune Algorithm, RBF network.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13281777 Imputing Missing Data in Electronic Health Records: A Comparison of Linear and Non-Linear Imputation Models
Authors: Alireza Vafaei Sadr, Vida Abedi, Jiang Li, Ramin Zand
Abstract:
Missing data is a common challenge in medical research and can lead to biased or incomplete results. When the data bias leaks into models, it further exacerbates health disparities; biased algorithms can lead to misclassification and reduced resource allocation and monitoring as part of prevention strategies for certain minorities and vulnerable segments of patient populations, which in turn further reduce data footprint from the same population – thus, a vicious cycle. This study compares the performance of six imputation techniques grouped into Linear and Non-Linear models, on two different real-world electronic health records (EHRs) datasets, representing 17864 patient records. The mean absolute percentage error (MAPE) and root mean squared error (RMSE) are used as performance metrics, and the results show that the Linear models outperformed the Non-Linear models in terms of both metrics. These results suggest that sometimes Linear models might be an optimal choice for imputation in laboratory variables in terms of imputation efficiency and uncertainty of predicted values.
Keywords: EHR, Machine Learning, imputation, laboratory variables, algorithmic bias.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 311776 The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation
Authors: N. Parandin, M. A. Fariborzi Araghi
Abstract:
in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13671775 Harmonic Pollution Caused by Non-Linear Load: Analysis and Identification
Authors: K. Khlifi, A. Haddouk, M. Hlaili, H. Mechergui
Abstract:
The present paper provides a detailed analysis of prior methods and approaches for non-linear load identification in residential buildings. The main goal of this analysis is to decipher the distorted signals and to estimate the harmonics influence on power systems. We have performed an analytical study of non-linear loads behavior in the residential environment. Simulations have been performed in order to evaluate the distorted rate of the current and follow his behavior. To complete this work, an instrumental platform has been realized to carry out practical tests on single-phase non-linear loads which illustrate the current consumption of some domestic appliances supplied with single-phase sinusoidal voltage. These non-linear loads have been processed and tracked in order to limit their influence on the power grid and to reduce the Joule effect losses. As a result, the study has allowed to identify responsible circuits of harmonic pollution.
Keywords: Distortion rate, harmonic analysis, harmonic pollution, non-linear load, power factor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7831774 A New Method to Solve a Non Linear Differential System
Authors: Seifedine Kadry
Abstract:
In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.
Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13411773 Some Results on Parallel Alternating Two-stage Methods
Authors: Guangbin Wang, Xue Li
Abstract:
In this paper, we present parallel alternating two-stage methods for solving linear system Ax=b, where A is a symmetric positive definite matrix. And we give some convergence results of these methods for nonsingular linear system.Keywords: alternating two-stage, convergence, linear system, parallel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11451772 State Feedback Controller Design via Takagi- Sugeno Fuzzy Model: LMI Approach
Authors: F. Khaber, K. Zehar, A. Hamzaoui
Abstract:
In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.
Keywords: Takagi-Sugeno fuzzy model, state feedback, linear matrix inequalities, robust stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24571771 Geometrically Non-Linear Axisymmetric Free Vibrations of Thin Isotropic Annular Plates
Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali
Abstract:
The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.
The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.
Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,
Keywords: Non-linear vibrations, Annular plates, Large vibration amplitudes.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22321770 Optimal Image Representation for Linear Canonical Transform Multiplexing
Authors: Navdeep Goel, Salvador Gabarda
Abstract:
Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4 × 4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4 × 4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4 × 4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain.Keywords: Chirp signals, Image multiplexing, Image transformation, Linear canonical transform, Polynomial approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20821769 The Stability of Almost n-multiplicative Maps in Fuzzy Normed Spaces
Authors: E. Ansari-Piri, N. Eghbali
Abstract:
Let A and B be two linear algebras. A linear map ϕ : A → B is called an n-homomorphism if ϕ(a1...an) = ϕ(a1)...ϕ(an) for all a1, ..., an ∈ A. In this note we have a verification on the behavior of almost n-multiplicative linear maps with n > 2 in the fuzzy normed spaces
Keywords: Almost multiplicative maps, n-homomorphism maps, almost n-multiplicative maps, fuzzy normed space, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12231768 Power System Security Assessment using Binary SVM Based Pattern Recognition
Authors: S Kalyani, K Shanti Swarup
Abstract:
Power System Security is a major concern in real time operation. Conventional method of security evaluation consists of performing continuous load flow and transient stability studies by simulation program. This is highly time consuming and infeasible for on-line application. Pattern Recognition (PR) is a promising tool for on-line security evaluation. This paper proposes a Support Vector Machine (SVM) based binary classification for static and transient security evaluation. The proposed SVM based PR approach is implemented on New England 39 Bus and IEEE 57 Bus systems. The simulation results of SVM classifier is compared with the other classifier algorithms like Method of Least Squares (MLS), Multi- Layer Perceptron (MLP) and Linear Discriminant Analysis (LDA) classifiers.Keywords: Static Security, Transient Security, Pattern Recognition, Classifier, Support Vector Machine.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18241767 Switching Rule for the Exponential Stability and Stabilization of Switched Linear Systems with Interval Time-varying Delays
Authors: Kreangkri Ratchagit
Abstract:
This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.
Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14791766 Convergence Analysis of the Generalized Alternating Two-Stage Method
Authors: Guangbin Wang, Liangliang Li, Fuping Tan
Abstract:
In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.
Keywords: Generalized alternating two-stage method, linear system, convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12191765 Stability of a Special Class of Switched Positive Systems
Authors: Xiuyong Ding, Lan Shu, Xiu Liu
Abstract:
This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.
Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14741764 Some Computational Results on MPI Parallel Implementation of Dense Simplex Method
Authors: El-Said Badr, Mahmoud Moussa, Konstantinos Paparrizos, Nikolaos Samaras, Angelo Sifaleras
Abstract:
There are two major variants of the Simplex Algorithm: the revised method and the standard, or tableau method. Today, all serious implementations are based on the revised method because it is more efficient for sparse linear programming problems. Moreover, there are a number of applications that lead to dense linear problems so our aim in this paper is to present some computational results on parallel implementation of dense Simplex Method. Our implementation is implemented on a SMP cluster using C programming language and the Message Passing Interface MPI. Preliminary computational results on randomly generated dense linear programs support our results.Keywords: Linear Programming, MPI, Parallel Implementation, Simplex Algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20061763 Internet Purchases in European Union Countries: Multiple Linear Regression Approach
Authors: Ksenija Dumičić, Anita Čeh Časni, Irena Palić
Abstract:
This paper examines economic and Information and Communication Technology (ICT) development influence on recently increasing Internet purchases by individuals for European Union member states. After a growing trend for Internet purchases in EU27 was noticed, all possible regression analysis was applied using nine independent variables in 2011. Finally, two linear regression models were studied in detail. Conducted simple linear regression analysis confirmed the research hypothesis that the Internet purchases in analyzed EU countries is positively correlated with statistically significant variable Gross Domestic Product per capita (GDPpc). Also, analyzed multiple linear regression model with four regressors, showing ICT development level, indicates that ICT development is crucial for explaining the Internet purchases by individuals, confirming the research hypothesis.
Keywords: European Union, Internet purchases, multiple linear regression model, outlier
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2899