**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3543

# Search results for: number of iteration

##### 3543 A Calibration Approach towards Reducing ASM2d Parameter Subsets in Phosphorus Removal Processes

**Authors:**
N.Boontian

**Abstract:**

**Keywords:**
ASM2d,
calibration approach,
iteration
methodology,
sensitivity,
phosphorus removal

##### 3542 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.

##### 3541 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.

##### 3540 Pattern Classification of Back-Propagation Algorithm Using Exclusive Connecting Network

**Authors:**
Insung Jung,
Gi-Nam Wang

**Abstract:**

**Keywords:**
Neural network,
Back-propagation,
classification.

##### 3539 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.

##### 3538 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.

##### 3537 Analytical Solutions of Kortweg-de Vries(KdV) Equation

**Authors:**
Foad Saadi,
M. Jalali Azizpour,
S.A. Zahedi

**Abstract:**

**Keywords:**
Variational Iteration Method (VIM),
HomotopyPerturbation Method (HPM),
Homotopy Analysis Method (HAM),
KdV Equation.

##### 3536 Enhanced Shell Sorting Algorithm

**Authors:**
Basit Shahzad,
Muhammad Tanvir Afzal

**Abstract:**

**Keywords:**
Algorithm,
Computation,
Shell,
Sorting.

##### 3535 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.

##### 3534 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.

##### 3533 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.

##### 3532 Periodic Storage Control Problem

**Authors:**
Ru-Shuo Sheu,
Han-Hsin Chou,
Te-Shyang Tan

**Abstract:**

**Keywords:**
periodic Markov decision process,
periodic
state,
policy-iteration algorithm.

##### 3531 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.

##### 3530 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.

##### 3529 A Kernel Classifier using Linearised Bregman Iteration

**Authors:**
K. A. D. N. K Wimalawarne

**Abstract:**

**Keywords:**
Compressive sensing,
Bregman iteration,
Generalisedhinge loss,
sparse,
kernels,
shrinkage functions

##### 3528 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

##### 3527 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.

##### 3526 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:**

**Keywords:**
5-DOF manipulator,
Inverse kinematics,
Iterative
algorithm,
Wrist offset.

##### 3525 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:**

**Keywords:**
Adam Block Method,
BDF,
Ordinary Differential
Equations,
Partitioning Block Intervalwise

##### 3524 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.

##### 3523 Numerical Optimization within Vector of Parameters Estimation in Volatility Models

**Authors:**
J. Arneric,
A. Rozga

**Abstract:**

**Keywords:**
Heteroscedasticity,
Log-likelihood Maximization,
Quasi-Newton iteration procedure,
Volatility.

##### 3522 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.

##### 3521 Computing the Loop Bound in Iterative Data Flow Graphs Using Natural Token Flow

**Authors:**
Ali Shatnawi

**Abstract:**

**Keywords:**
Data flow graph,
Iteration period bound,
Rateoptimalscheduling,
Recursive DSP algorithms.

##### 3520 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.

##### 3519 Two-step Iterative Process For Common Fixed Points of Two Asymptotically Quasi-nonexpansive Mappings

**Authors:**
Safeer Hussain Khan

**Abstract:**

**Keywords:**
Asypmtotically quasi-nonexpansive mappings,
Commonfixed point,
Strong and weak convergence,
Iteration process.

##### 3518 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.

##### 3517 Effects of Introducing Similarity Measures into Artificial Bee Colony Approach for Optimization of Vehicle Routing Problem

**Authors:**
P. Shunmugapriya,
S. Kanmani,
P. Jude Fredieric,
U. Vignesh,
J. Reman Justin,
K. Vivek

**Abstract:**

Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem and it is quite difficult to find an optimal solution consisting of a set of routes for vehicles whose total cost is minimum. Evolutionary and swarm intelligent (SI) algorithms play a vital role in solving optimization problems. While the SI algorithms perform search, the diversity between the solutions they exploit is very important. This is because of the need to avoid early convergence and to get an appropriate balance between the exploration and exploitation. Therefore, it is important to check how far the solutions are diverse. In this paper, we measure the similarity between solutions, which ABC exploits while optimizing VRP. The similar solutions found are discarded at the end of the iteration and only unique solutions are passed on to the next iteration. The bees of discarded solutions become scouts and they start searching for new solutions. This process is continued and results show that the solution is optimized at lesser number of iterations but with the overhead of computing similarity in all the iterations. The problem instance from Solomon benchmarked dataset has been used for evaluating the presented methodology.

**Keywords:**
ABC algorithm,
vehicle routing problem,
optimization,
Jaccard’s similarity measure.

##### 3516 Trajectory-Based Modified Policy Iteration

**Abstract:**

**Keywords:**
Markov Decision Process (MDP),
Mobile robot,
Policy iteration,
Simulation.

##### 3515 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

##### 3514 Application of Load Transfer Technique for Distribution Power Flow Analysis

**Authors:**
Udomsak Thongkrajay,
Padej Pao-La-Or,
Thanatchai Kulworawanichpong

**Abstract:**

**Keywords:**
Load transfer technique,
Newton-Raphson power flow,
ill-condition