Search results for: Bregman iteration
125 A Kernel Classifier using Linearised Bregman Iteration
Authors: K. A. D. N. K Wimalawarne
Abstract:
In this paper we introduce a novel kernel classifier based on a iterative shrinkage algorithm developed for compressive sensing. We have adopted Bregman iteration with soft and hard shrinkage functions and generalized hinge loss for solving l1 norm minimization problem for classification. Our experimental results with face recognition and digit classification using SVM as the benchmark have shown that our method has a close error rate compared to SVM but do not perform better than SVM. We have found that the soft shrinkage method give more accuracy and in some situations more sparseness than hard shrinkage methods.Keywords: Compressive sensing, Bregman iteration, Generalisedhinge loss, sparse, kernels, shrinkage functions
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1369124 Iteration Acceleration for Nonlinear Coupled Parabolic-Hyperbolic System
Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue
Abstract:
A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.
Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1547123 Variational Iteration Method for the Solution of Boundary Value Problems
Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.
Abstract:
In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.
Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2085122 Convergence of a One-step Iteration Scheme for Quasi-asymptotically Nonexpansive Mappings
Authors: Safeer Hussain Khan
Abstract:
In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.
Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1434121 Performance Analysis of Reconstruction Algorithms in Diffuse Optical Tomography
Authors: K. Uma Maheswari, S. Sathiyamoorthy, G. Lakshmi
Abstract:
Diffuse Optical Tomography (DOT) is a non-invasive imaging modality used in clinical diagnosis for earlier detection of carcinoma cells in brain tissue. It is a form of optical tomography which produces gives the reconstructed image of a human soft tissue with by using near-infra-red light. It comprises of two steps called forward model and inverse model. The forward model provides the light propagation in a biological medium. The inverse model uses the scattered light to collect the optical parameters of human tissue. DOT suffers from severe ill-posedness due to its incomplete measurement data. So the accurate analysis of this modality is very complicated. To overcome this problem, optical properties of the soft tissue such as absorption coefficient, scattering coefficient, optical flux are processed by the standard regularization technique called Levenberg - Marquardt regularization. The reconstruction algorithms such as Split Bregman and Gradient projection for sparse reconstruction (GPSR) methods are used to reconstruct the image of a human soft tissue for tumour detection. Among these algorithms, Split Bregman method provides better performance than GPSR algorithm. The parameters such as signal to noise ratio (SNR), contrast to noise ratio (CNR), relative error (RE) and CPU time for reconstructing images are analyzed to get a better performance.
Keywords: Diffuse optical tomography, ill-posedness, Levenberg Marquardt method, Split Bregman, the Gradient projection for sparse reconstruction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1600120 On Algebraic Structure of Improved Gauss-Seidel Iteration
Authors: O. M. Bamigbola, A. A. Ibrahim
Abstract:
Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.
Keywords: Linear system of equations, Gauss-Seidel iteration, algebraic structure, convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2914119 Periodic Storage Control Problem
Authors: Ru-Shuo Sheu, Han-Hsin Chou, Te-Shyang Tan
Abstract:
Considering a reservoir with periodic states and different cost functions with penalty, its release rules can be modeled as a periodic Markov decision process (PMDP). First, we prove that policy- iteration algorithm also works for the PMDP. Then, with policy- iteration algorithm, we obtain the optimal policies for a special aperiodic reservoir model with two cost functions under large penalty and give a discussion when the penalty is small.Keywords: periodic Markov decision process, periodic state, policy-iteration algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1229118 Weak Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space
Authors: Alemayehu Geremew Negash
Abstract:
We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.
Keywords: Common fixed point, Mann iteration, Multivalued mapping, weak convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1623117 A Contractor Iteration Method Using Eigenpairs for Positive Solutions of Nonlinear Elliptic Equation
Authors: Hailong Zhu, Zhaoxiang Li, Kejun Zhuang
Abstract:
By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.
Keywords: Positive solutions, newton's method, contractor iteration method, Eigenpairs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1365116 A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations
Authors: Jinfeng Wang, Yang Liu, Hong Li
Abstract:
In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.
Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2125115 Managing Iterations in Product Design and Development
Authors: K. Aravindhan, Trishit Bandyopadhyay, Mahesh Mehendale, Supriya Kumar De
Abstract:
The inherent iterative nature of product design and development poses significant challenge to reduce the product design and development time (PD). In order to shorten the time to market, organizations have adopted concurrent development where multiple specialized tasks and design activities are carried out in parallel. Iterative nature of work coupled with the overlap of activities can result in unpredictable time to completion and significant rework. Many of the products have missed the time to market window due to unanticipated or rather unplanned iteration and rework. The iterative and often overlapped processes introduce greater amounts of ambiguity in design and development, where the traditional methods and tools of project management provide less value. In this context, identifying critical metrics to understand the iteration probability is an open research area where significant contribution can be made given that iteration has been the key driver of cost and schedule risk in PD projects. Two important questions that the proposed study attempts to address are: Can we predict and identify the number of iterations in a product development flow? Can we provide managerial insights for a better control over iteration? The proposal introduces the concept of decision points and using this concept intends to develop metrics that can provide managerial insights into iteration predictability. By characterizing the product development flow as a network of decision points, the proposed research intends to delve further into iteration probability and attempts to provide more clarity.
Keywords: Decision Points, Iteration, Product Design, Rework.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2179114 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations
Authors: Sara Barati, Karim Ivaz
Abstract:
In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.
Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2461113 Development Partitioning Intervalwise Block Method for Solving Ordinary Differential Equations
Authors: K.H.Khairul Anuar, K.I.Othman, F.Ishak, Z.B.Ibrahim, Z.Majid
Abstract:
Solving Ordinary Differential Equations (ODEs) by using Partitioning Block Intervalwise (PBI) technique is our aim in this paper. The PBI technique is based on Block Adams Method and Backward Differentiation Formula (BDF). Block Adams Method only use the simple iteration for solving while BDF requires Newtonlike iteration involving Jacobian matrix of ODEs which consumes a considerable amount of computational effort. Therefore, PBI is developed in order to reduce the cost of iteration within acceptable maximum errorKeywords: Adam Block Method, BDF, Ordinary Differential Equations, Partitioning Block Intervalwise
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1658112 A Calibration Approach towards Reducing ASM2d Parameter Subsets in Phosphorus Removal Processes
Authors: N.Boontian
Abstract:
A novel calibration approach that aims to reduce ASM2d parameter subsets and decrease the model complexity is presented. This approach does not require high computational demand and reduces the number of modeling parameters required to achieve the ASMs calibration by employing a sensitivity and iteration methodology. Parameter sensitivity is a crucial factor and the iteration methodology enables refinement of the simulation parameter values. When completing the iteration process, parameters values are determined in descending order of their sensitivities. The number of iterations required is equal to the number of model parameters of the parameter significance ranking. This approach was used for the ASM2d model to the evaluated EBPR phosphorus removal and it was successful. Results of the simulation provide calibration parameters. These included YPAO, YPO4, YPHA, qPHA, qPP, μPAO, bPAO, bPP, bPHA, KPS, YA, μAUT, bAUT, KO2 AUT, and KNH4 AUT. Those parameters were corresponding to the experimental data available.Keywords: ASM2d, calibration approach, iteration methodology, sensitivity, phosphorus removal
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2407111 An Analytical Method to Analysis of Foam Drainage Problem
Authors: A. Nikkar, M. Mighani
Abstract:
In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.
Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1799110 Optimal Design of UPFC Based Damping Controller Using Iteration PSO
Authors: Amin Safari, Hossein Shayeghi
Abstract:
This paper presents a novel approach for tuning unified power flow controller (UPFC) based damping controller in order to enhance the damping of power system low frequency oscillations. The design problem of damping controller is formulated as an optimization problem according to the eigenvalue-based objective function which is solved using iteration particle swarm optimization (IPSO). The effectiveness of the proposed controller is demonstrated through eigenvalue analysis and nonlinear time-domain simulation studies under a wide range of loading conditions. The simulation study shows that the designed controller by IPSO performs better than CPSO in finding the solution. Moreover, the system performance analysis under different operating conditions show that the δE based controller is superior to the mB based controller.
Keywords: UPFC, Optimization Problem, Iteration ParticleSwarm Optimization, Damping Controller, Low FrequencyOscillations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1794109 Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising
Authors: Jianwei Ma, Diriba Gemechu
Abstract:
In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm.Keywords: Anisotropic total fractional order variation, fractional order bounded variation, seismic random noise attenuation, Split Bregman Algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 997108 Computing the Loop Bound in Iterative Data Flow Graphs Using Natural Token Flow
Authors: Ali Shatnawi
Abstract:
Signal processing applications which are iterative in nature are best represented by data flow graphs (DFG). In these applications, the maximum sampling frequency is dependent on the topology of the DFG, the cyclic dependencies in particular. The determination of the iteration bound, which is the reciprocal of the maximum sampling frequency, is critical in the process of hardware implementation of signal processing applications. In this paper, a novel technique to compute the iteration bound is proposed. This technique is different from all previously proposed techniques, in the sense that it is based on the natural flow of tokens into the DFG rather than the topology of the graph. The proposed algorithm has lower run-time complexity than all known algorithms. The performance of the proposed algorithm is illustrated through analytical analysis of the time complexity, as well as through simulation of some benchmark problems.Keywords: Data flow graph, Iteration period bound, Rateoptimalscheduling, Recursive DSP algorithms.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2555107 Kalman Filter Gain Elimination in Linear Estimation
Authors: Nicholas D. Assimakis
Abstract:
In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.
Keywords: Discrete time, linear estimation, Kalman filter, Kalman filter gain.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 616106 Two-step Iterative Process For Common Fixed Points of Two Asymptotically Quasi-nonexpansive Mappings
Authors: Safeer Hussain Khan
Abstract:
In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.Keywords: Asypmtotically quasi-nonexpansive mappings, Commonfixed point, Strong and weak convergence, Iteration process.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1525105 Analytical Solutions of Kortweg-de Vries(KdV) Equation
Authors: Foad Saadi, M. Jalali Azizpour, S.A. Zahedi
Abstract:
The objective of this paper is to present a comparative study of Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM) for the semi analytical solution of Kortweg-de Vries (KdV) type equation called KdV. The study have been highlighted the efficiency and capability of aforementioned methods in solving these nonlinear problems which has been arisen from a number of important physical phenomenon.Keywords: Variational Iteration Method (VIM), HomotopyPerturbation Method (HPM), Homotopy Analysis Method (HAM), KdV Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2357104 Vibration of a Beam on an Elastic Foundation Using the Variational Iteration Method
Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger
Abstract:
Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.
Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 950103 Investigation of a Transition from Steady Convection to Chaos in Porous Media Using Piecewise Variational Iteration Method
Authors: Mohamed M. Mousa, Aidarkhan Kaltayev Shahwar F. Ragab
Abstract:
In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.
Keywords: Variational iteration method, free convection, Chaos, Lorenz equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1521102 Trajectory-Based Modified Policy Iteration
Abstract:
This paper presents a new problem solving approach that is able to generate optimal policy solution for finite-state stochastic sequential decision-making problems with high data efficiency. The proposed algorithm iteratively builds and improves an approximate Markov Decision Process (MDP) model along with cost-to-go value approximates by generating finite length trajectories through the state-space. The approach creates a synergy between an approximate evolving model and approximate cost-to-go values to produce a sequence of improving policies finally converging to the optimal policy through an intelligent and structured search of the policy space. The approach modifies the policy update step of the policy iteration so as to result in a speedy and stable convergence to the optimal policy. We apply the algorithm to a non-holonomic mobile robot control problem and compare its performance with other Reinforcement Learning (RL) approaches, e.g., a) Q-learning, b) Watkins Q(λ), c) SARSA(λ).Keywords: Markov Decision Process (MDP), Mobile robot, Policy iteration, Simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1431101 Numerical Algorithms for Solving a Type of Nonlinear Integro-Differential Equations
Authors: Shishen Xie
Abstract:
In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations
Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2111100 Comparison of Newton Raphson and Gauss Seidel Methods for Power Flow Analysis
Authors: H. Abaali, T. Talbi, R.Skouri
Abstract:
This paper presents a comparative study of the Gauss Seidel and Newton-Raphson polar coordinates methods for power flow analysis. The effectiveness of these methods are evaluated and tested through a different IEEE bus test system on the basis of number of iteration, computational time, tolerance value and convergence.
Keywords: Convergence time, Gauss-Seidel Method, Newton-Raphson Method, number of iteration, power flow analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 251099 Pattern Classification of Back-Propagation Algorithm Using Exclusive Connecting Network
Authors: Insung Jung, Gi-Nam Wang
Abstract:
The objective of this paper is to a design of pattern classification model based on the back-propagation (BP) algorithm for decision support system. Standard BP model has done full connection of each node in the layers from input to output layers. Therefore, it takes a lot of computing time and iteration computing for good performance and less accepted error rate when we are doing some pattern generation or training the network. However, this model is using exclusive connection in between hidden layer nodes and output nodes. The advantage of this model is less number of iteration and better performance compare with standard back-propagation model. We simulated some cases of classification data and different setting of network factors (e.g. hidden layer number and nodes, number of classification and iteration). During our simulation, we found that most of simulations cases were satisfied by BP based using exclusive connection network model compared to standard BP. We expect that this algorithm can be available to identification of user face, analysis of data, mapping data in between environment data and information.Keywords: Neural network, Back-propagation, classification.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 164498 An Iterative Algorithm for Inverse Kinematics of 5-DOF Manipulator with Offset Wrist
Authors: Juyi Park, Jung-Min Kim, Hee-Hwan Park, Jin-Wook Kim, Gye-Hyung Kang, Soo-Ho Kim
Abstract:
This paper presents an iterative algorithm to find a inverse kinematic solution of 5-DOF robot. The algorithm is to minimize the iteration number. Since the 5-DOF robot cannot give full orientation of tool. Only z-direction of tool is satisfied while rotation of tool is determined by kinematic constraint. This work therefore described how to specify the tool direction and let the tool rotation free. The simulation results show that this algorithm effectively worked. Using the proposed iteration algorithm, error due to inverse kinematics converged to zero rapidly in 5 iterations. This algorithm was applied in real welding robot and verified through various practical works.Keywords: 5-DOF manipulator, Inverse kinematics, Iterative algorithm, Wrist offset.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 411997 An Efficient Backward Semi-Lagrangian Scheme for Nonlinear Advection-Diffusion Equation
Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim
Abstract:
In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.
Keywords: Semi-Lagrangian method, Iteration free method, Nonlinear advection-diffusion equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 247296 Numerical Optimization within Vector of Parameters Estimation in Volatility Models
Authors: J. Arneric, A. Rozga
Abstract:
In this paper usefulness of quasi-Newton iteration procedure in parameters estimation of the conditional variance equation within BHHH algorithm is presented. Analytical solution of maximization of the likelihood function using first and second derivatives is too complex when the variance is time-varying. The advantage of BHHH algorithm in comparison to the other optimization algorithms is that requires no third derivatives with assured convergence. To simplify optimization procedure BHHH algorithm uses the approximation of the matrix of second derivatives according to information identity. However, parameters estimation in a/symmetric GARCH(1,1) model assuming normal distribution of returns is not that simple, i.e. it is difficult to solve it analytically. Maximum of the likelihood function can be founded by iteration procedure until no further increase can be found. Because the solutions of the numerical optimization are very sensitive to the initial values, GARCH(1,1) model starting parameters are defined. The number of iterations can be reduced using starting values close to the global maximum. Optimization procedure will be illustrated in framework of modeling volatility on daily basis of the most liquid stocks on Croatian capital market: Podravka stocks (food industry), Petrokemija stocks (fertilizer industry) and Ericsson Nikola Tesla stocks (information-s-communications industry).Keywords: Heteroscedasticity, Log-likelihood Maximization, Quasi-Newton iteration procedure, Volatility.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2633