**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1251

# Search results for: conjugate gradient coefficient

##### 1251 A New Modification of Nonlinear Conjugate Gradient Coefficients with Global Convergence Properties

**Authors:**
Ahmad Alhawarat,
Mustafa Mamat,
Mohd Rivaie,
Ismail Mohd

**Abstract:**

**Keywords:**
Conjugate gradient method,
conjugate gradient
coefficient,
global convergence.

##### 1250 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

*AXB=C*and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

**Keywords:**
Iterative method,
symmetric arrowhead matrix,
conjugate gradient algorithm.

##### 1249 An Improved Conjugate Gradient Based Learning Algorithm for Back Propagation Neural Networks

**Authors:**
N. M. Nawi,
R. S. Ransing,
M. R. Ransing

**Abstract:**

The conjugate gradient optimization algorithm is combined with the modified back propagation algorithm to yield a computationally efficient algorithm for training multilayer perceptron (MLP) networks (CGFR/AG). The computational efficiency is enhanced by adaptively modifying initial search direction as described in the following steps: (1) Modification on standard back propagation algorithm by introducing a gain variation term in the activation function, (2) Calculation of the gradient descent of error with respect to the weights and gains values and (3) the determination of a new search direction by using information calculated in step (2). The performance of the proposed method is demonstrated by comparing accuracy and computation time with the conjugate gradient algorithm used in MATLAB neural network toolbox. The results show that the computational efficiency of the proposed method was better than the standard conjugate gradient algorithm.

**Keywords:**
Adaptive gain variation,
back-propagation,
activation function,
conjugate gradient,
search direction.

##### 1248 Comparison of Three Versions of Conjugate Gradient Method in Predicting an Unknown Irregular Boundary Profile

**Authors:**
V. Ghadamyari,
F. Samadi,
F. Kowsary

**Abstract:**

**Keywords:**
Boundary elements,
Conjugate Gradient Method,
Inverse Geometry Problem,
Sensitivity equation.

##### 1247 Advanced Neural Network Learning Applied to Pulping Modeling

**Authors:**
Z. Zainuddin,
W. D. Wan Rosli,
R. Lanouette,
S. Sathasivam

**Abstract:**

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulping problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified odified problem M-1 Ax= M-1b where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

**Keywords:**
Convergence,
pulping modeling,
neural networks,
preconditioned conjugate gradient.

##### 1246 Modeling of Pulping of Sugar Maple Using Advanced Neural Network Learning

**Authors:**
W. D. Wan Rosli,
Z. Zainuddin,
R. Lanouette,
S. Sathasivam

**Abstract:**

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

**Keywords:**
Convergence,
Modeling,
Neural Networks,
Preconditioned Conjugate Gradient.

##### 1245 Signature Recognition Using Conjugate Gradient Neural Networks

**Authors:**
Jamal Fathi Abu Hasna

**Abstract:**

**Keywords:**
Signature Verification,
MATLAB Software,
Conjugate Gradient,
Segmentation,
Skilled Forgery,
and Genuine.

##### 1244 On the Algorithmic Iterative Solutions of Conjugate Gradient, Gauss-Seidel and Jacobi Methods for Solving Systems of Linear Equations

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
H. N. Ude

**Abstract:**

In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

**Keywords:**
conjugate gradient,
linear equations,
symmetric and positive definite matrix,
Gauss-Seidel,
Jacobi,
algorithm

##### 1243 An Improved Learning Algorithm based on the Conjugate Gradient Method for Back Propagation Neural Networks

**Authors:**
N. M. Nawi,
M. R. Ransing,
R. S. Ransing

**Abstract:**

**Keywords:**
Back-propagation,
activation function,
conjugategradient,
search direction,
gain variation.

##### 1242 A Study on Neural Network Training Algorithm for Multiface Detection in Static Images

**Authors:**
Zulhadi Zakaria,
Nor Ashidi Mat Isa,
Shahrel A. Suandi

**Abstract:**

**Keywords:**
training algorithm,
multiface,
static image,
neural network

##### 1241 Parallel Pipelined Conjugate Gradient Algorithm on Heterogeneous Platforms

**Authors:**
Sergey Kopysov,
Nikita Nedozhogin,
Leonid Tonkov

**Abstract:**

The article presents a parallel iterative solver for large sparse linear systems which can be used on a heterogeneous platform. Traditionally, the problem of solving linear systems do not scale well on cluster containing multiple Central Processing Units (multi-CPUs cluster) or cluster containing multiple Graphics Processing Units (multi-GPUs cluster). For example, most of the attempts to implement the classical conjugate gradient method were at best counted in the same amount of time as the problem was enlarged. The paper proposes the pipelined variant of the conjugate gradient method (PCG), a formulation that is potentially better suited for hybrid CPU/GPU computing since it requires only one synchronization point per one iteration, instead of two for standard CG (Conjugate Gradient). The standard and pipelined CG methods need the vector entries generated by current GPU and other GPUs for matrix-vector product. So the communication between GPUs becomes a major performance bottleneck on miltiGPU cluster. The article presents an approach to minimize the communications between parallel parts of algorithms. Additionally, computation and communication can be overlapped to reduce the impact of data exchange. Using pipelined version of the CG method with one synchronization point, the possibility of asynchronous calculations and communications, load balancing between the CPU and GPU for solving the large linear systems allows for scalability. The algorithm is implemented with the combined use of technologies: MPI, OpenMP and CUDA. We show that almost optimum speed up on 8-CPU/2GPU may be reached (relatively to a one GPU execution). The parallelized solver achieves a speedup of up to 5.49 times on 16 NVIDIA Tesla GPUs, as compared to one GPU.

**Keywords:**
Conjugate Gradient,
GPU,
parallel programming,
pipelined algorithm.

##### 1240 A Finite-Time Consensus Protocol of the Multi-Agent Systems

**Authors:**
Xin-Lei Feng,
Ting-Zhu Huang

**Abstract:**

According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.

**Keywords:**
Consensus protocols; Graph theory; Multi-agent systems;Conjugate gradient algorithm; Finite-time.

##### 1239 Bending Gradient Coefficient Correction for I-Beams

**Authors:**
H. R. Kazemi Nia,
A. Yeganeh Fallah

**Abstract:**

**Keywords:**
Beams critical moment,
Bending Gradient Coefficient,
finite element,
Lateral Torsional Buckling

##### 1238 Bayesian Inference for Phase Unwrapping Using Conjugate Gradient Method in One and Two Dimensions

**Authors:**
Yohei Saika,
Hiroki Sakaematsu,
Shota Akiyama

**Abstract:**

We investigated statistical performance of Bayesian inference using maximum entropy and MAP estimation for several models which approximated wave-fronts in remote sensing using SAR interferometry. Using Monte Carlo simulation for a set of wave-fronts generated by assumed true prior, we found that the method of maximum entropy realized the optimal performance around the Bayes-optimal conditions by using model of the true prior and the likelihood representing optical measurement due to the interferometer. Also, we found that the MAP estimation regarded as a deterministic limit of maximum entropy almost achieved the same performance as the Bayes-optimal solution for the set of wave-fronts. Then, we clarified that the MAP estimation perfectly carried out phase unwrapping without using prior information, and also that the MAP estimation realized accurate phase unwrapping using conjugate gradient (CG) method, if we assumed the model of the true prior appropriately.

**Keywords:**
Bayesian inference using maximum entropy,
MAP
estimation using conjugate gradient method,
SAR interferometry.

##### 1237 Developing a Conjugate Heat Transfer Solver

**Authors:**
Mansour A. Al Qubeissi

**Abstract:**

The current paper presents a numerical approach in solving the conjugate heat transfer problems. A heat conduction code is coupled internally with a computational fluid dynamics solver for developing a couple conjugate heat transfer solver. Methodology of treating non-matching meshes at interface has also been proposed. The validation results of 1D and 2D cases for the developed conjugate heat transfer code have shown close agreement with the solutions given by analysis.

**Keywords:**
Computational Fluid Dynamics,
Conjugate Heat transfer,
Heat Conduction,
Heat Transfer

##### 1236 Loudspeaker Parameters Inverse Problem for Improving Sound Frequency Response Simulation

**Authors:**
Y. T. Tsai,
Jin H. Huang

**Abstract:**

The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

**Keywords:**
Inverse problem,
cone effective area,
loudspeaker,
nonlinear conjugate gradient method.

##### 1235 Beam Orientation Optimization Using Ant Colony Optimization in Intensity Modulated Radiation Therapy

**Authors:**
Xi Pei,
Ruifen Cao,
Hui Liu,
Chufeng Jin,
Mengyun Cheng,
Huaqing Zheng,
Yican Wu,
FDS Team

**Abstract:**

**Keywords:**
intensity modulated radiation therapy,
ant colonyoptimization,
Conjugate Gradient algorithm

##### 1234 GPS TEC Variation Affected by the Interhemispheric Conjugate Auroral Activity on 21 September 2009

**Authors:**
W. Suparta,
M. A. Mohd. Ali,
M. S. Jit Singh,
B. Yatim,
T. Motoba,
N. Sato,
A. Kadokura,
G. Bjornsson

**Abstract:**

**Keywords:**
Auroral activity,
GPS TEC,
Interhemispheric
conjugate points,
Responses

##### 1233 A Comparison of First and Second Order Training Algorithms for Artificial Neural Networks

**Authors:**
Syed Muhammad Aqil Burney,
Tahseen Ahmed Jilani,
C. Ardil

**Abstract:**

**Keywords:**
Backpropagation algorithm,
conjugacy condition,
line search,
matrix perturbation

##### 1232 Coefficients of Some Double Trigonometric Cosine and Sine Series

**Authors:**
Jatinderdeep Kaur

**Abstract:**

**Keywords:**
Conjugate Dirichlet kernel,
conjugate Fejer kernel,
Fourier series,
Semi-convexity.

##### 1231 Implementation of Neural Network Based Electricity Load Forecasting

**Authors:**
Myint Myint Yi,
Khin Sandar Linn,
Marlar Kyaw

**Abstract:**

**Keywords:**
Neural network,
Load forecast,
Time series,
wavelettransform.

##### 1230 Mathematical Modeling of the Working Principle of Gravity Gradient Instrument

**Authors:**
Danni Cong,
Meiping Wu,
Hua Mu,
Xiaofeng He,
Junxiang Lian,
Juliang Cao,
Shaokun Cai,
Hao Qin

**Abstract:**

**Keywords:**
Gravity gradient,
accelerometer,
gravity gradient sensor,
single-axis rotation modulation.

##### 1229 Simulating Gradient Contour and Mesh of a Scalar Field

**Authors:**
Usman Ali Khan,
Bismah Tariq,
Khalida Raza,
Saima Malik,
Aoun Muhammad

**Abstract:**

**Keywords:**
MATLAB,
Gradient,
Contour,
Scalar Field,
Mesh

##### 1228 Numerical Investigation of Aerodynamic Analysis on Passenger Vehicle

**Authors:**
Cafer Görkem Pınar,
İlker Coşar,
Serkan Uzun,
Atahan Çelebi,
Mehmet Ali Ersoy,
Ali Pınarbaşı

**Abstract:**

In this study, it was numerically investigated that a 1:1 scale model of the Renault Clio MK4 SW brand vehicle aerodynamic analysis was performed in the commercial computational fluid dynamics (CFD) package program of ANSYS CFX 2021 R1 under steady, subsonic, and 3-D conditions. The model of vehicle used for the analysis was made independent of the number of mesh elements and the k-epsilon turbulence model was applied during the analysis. Results were interpreted as streamlines, pressure gradient, and turbulent kinetic energy contours around the vehicle at 50 km/h and 100 km/h speeds. In addition, the validity of the analysis was decided by comparing the drag coefficient of the vehicle with the values in the literature. As a result, the pressure gradient contours of the taillight of the Renault Clio MK4 SW vehicle were examined and the behavior of the total force at speeds of 50 km/h and 100 km/h was interpreted.

**Keywords:**
CFD,
k-epsilon,
aerodynamics,
drag coefficient,
taillight.

##### 1227 Conjugate Heat and Mass Transfer for MHD Mixed Convection with Viscous Dissipation and Radiation Effect for Viscoelastic Fluid past a Stretching Sheet

**Authors:**
Kai-Long Hsiao,
BorMing Lee

**Abstract:**

**Keywords:**
Conjugate heat and mass transfer,
Radiation effect,
Magnetic effect,
Viscoelastic fluid,
Viscous dissipation,
Stretchingsheet.

##### 1226 Conjugate Free Convection in a Square Cavity Filled with Nanofluid and Heated from Below by Spatial Wall Temperature

**Authors:**
Ishak Hashim,
Ammar Alsabery

**Abstract:**

**Keywords:**
Conjugate free convection,
nanofluid,
spatial
temperature.

##### 1225 Research on the Correlation of the Fluctuating Density Gradient of the Compressible Flows

**Authors:**
Yasuo Obikane

**Abstract:**

**Keywords:**
Turbulence Modeling ,
Density Gradient Correlation,
Compressible

##### 1224 Conjugate Heat transfer over an Unsteady Stretching Sheet Mixed Convection with Magnetic Effect

**Authors:**
Kai-Long Hsiao

**Abstract:**

**Keywords:**
Finite-difference method,
Conjugate heat transfer,
Unsteady Stretching Sheet,
MHD,
Mixed convection.

##### 1223 Segmentation of Noisy Digital Images with Stochastic Gradient Kernel

**Authors:**
Abhishek Neogi,
Jayesh Verma,
Pinaki Pratim Acharjya

**Abstract:**

**Keywords:**
Image segmentation,
edge Detection,
noisy images,
spatialfilters,
stochastic gradient kernel.

##### 1222 Dynamic Measurement System Modeling with Machine Learning Algorithms

**Authors:**
Changqiao Wu,
Guoqing Ding,
Xin Chen

**Abstract:**

**Keywords:**
Dynamic system modeling,
neural network,
normal
equation,
second order gradient descent.