**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**336

# Search results for: Conjugate Gradient

##### 336 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.

##### 335 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.

##### 334 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.

##### 333 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.

##### 332 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.

##### 331 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.

##### 330 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.

##### 329 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

##### 328 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.

##### 327 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

##### 326 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.

##### 325 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.

##### 324 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.

##### 323 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

##### 322 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.

##### 321 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

##### 320 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

##### 319 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

##### 318 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.

##### 317 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

##### 316 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.

##### 315 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.

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

**Authors:**
Yasuo Obikane

**Abstract:**

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

##### 313 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.

##### 312 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.

##### 311 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.

##### 310 Green Function and Eshelby Tensor Based on Mindlin’s 2nd Gradient Model: An Explicit Study of Spherical Inclusion Case

**Authors:**
A. Selmi,
A. Bisharat

**Abstract:**

Using Fourier transform and based on the Mindlin's 2^{nd} gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.

**Keywords:**
Eshelby tensor,
Eshelby-like tensor,
Green’s function,
Mindlin’s 2nd gradient model,
Spherical inclusion.

##### 309 An Iterative Algorithm for KLDA Classifier

**Authors:**
D.N. Zheng,
J.X. Wang,
Y.N. Zhao,
Z.H. Yang

**Abstract:**

**Keywords:**
Linear discriminant analysis (LDA),
kernel LDA
(KLDA),
conjugate gradient algorithm,
nonlinear discriminant classifier.

##### 308 Flexural Strength Design of RC Beams with Consideration of Strain Gradient Effect

**Authors:**
Mantai Chen,
Johnny Ching Ming Ho

**Abstract:**

The stress-strain relationship of concrete under flexure is one of the essential parameters in assessing ultimate flexural strength capacity of RC beams. Currently, the concrete stress-strain curve in flexure is obtained by incorporating a constant scale-down factor of 0.85 in the uniaxial stress-strain curve. However, it was revealed that strain gradient would improve the maximum concrete stress under flexure and concrete stress-strain curve is strain gradient dependent. Based on the strain-gradient-dependent concrete stress-strain curve, the investigation of the combined effects of strain gradient and concrete strength on flexural strength of RC beams was extended to high strength concrete up to 100 MPa by theoretical analysis. As an extension and application of the authors’ previous study, a new flexural strength design method incorporating the combined effects of strain gradient and concrete strength is developed. A set of equivalent rectangular concrete stress block parameters is proposed and applied to produce a series of design charts showing that the flexural strength of RC beams are improved with strain gradient effect considered.

**Keywords:**
Beams,
Equivalent concrete stress block,
Flexural strength,
Strain gradient.

##### 307 Constructal Enhancement of Fins Design Integrated to Phase Change Materials

**Authors:**
Varun Joshi,
Manish K. Rathod

**Abstract:**

**Keywords:**
Constructal theory,
enthalpy porosity approach,
phase change materials,
fins.