The conjugate gradient method plays a very important role in several fields, to solve problems of large sizes. To improve the efficiency of this method, a lot of work has been done; in this paper, we propose a new modification of PRP method to solve a large scale unconstrained optimization problems in relation with strong Wolf Powell Line Search property, when the latter was used under some conditions, a global convergence result was proved. In comparison with other known methods the efficiency of this method proved that it is better in the number of iterations and in time on $90$ proposed problems by use of Matlab.

Decision Neural Network is a new approach for solving multi-objective decision-making problems based on artificial neural networks. Using inaccurate evaluation data, network training has improved and the number of educational data sets has decreased. The available training method is based on the gradient decent method (BP). One of its limitations is related to its convergence speed. Therefore, decision makers can simply guess the necessary data. In this paper, for increasing the Decision Neural Network training efficiency, a conjugate gradient based method has developed for network training. The key point in decision neural network training is to keep the same structures and parameters of the two sub network (multilayer perceptron) through training process. The efficiency of the proposed method is evaluated by estimating linear and nonlinear utility function of multi-objective decision problems. The results of the proposed method are compared with previous existing method and show that in the proposed method, convergence is faster than previous methods and the results are more favorable.

In this paper, the conjugate gradient (CG) method is employed for identifying the parameters of crack in a functionally graded beam from natural frequency measurement. The crack is modeled as a massless rotational spring with sectional flexibility. Using the Euler-Bernoulli beam theory on two separate beams and applying the compatibility requirements of the crack, the characteristic equation can be obtained as a function of natural frequency and location and depth of crack. In direct problem, the natural frequency is computed using analytical analysis. Moreover, the location and depth of crack are determined by measuring the three natural frequencies of beam in inverse problem. In this study, the CG method is utilized in inverse problem to determine the location and depth of crack. The obtained results show the efficiency of CG algorithm in terms of accuracy and the convergence speed.

Usage of spatial information in the DOA estimation of signals, overcome some weaknesses of time-processing techniques. In this paper, following the Direct Data Domain Least Square (D3LS) technique, amplitude information of signals arrived at each element in an antenna array are arranged in a square matrix in which, except for the first row, other entries are combinations of reflective signals, noise and interference. By forming an equation including this matrix, weighting factors of antenna array, and antenna gain, coefficients are calculated in such a way that all signals which their DOA is not important, i.e. reflected signals, noise and etc., reach their least quantity. Then, by making a symmetric square matrix and modification of the main equation according to Linear Conjugate Gradient procedure, weighting factors of antenna are obtained. Finally, it is shown by simulation that this procedure will accelerate the convergence process remarkably compared with D3LS technique.

The System of Ax=b in which A is a Toeplitz and symmetric positive definite (SPD) is derived from convolution-type integral equations. At normal state, the system contains in appropriate eigenvalues not clustering around 1. In the present paper, the preconditioned CG method is used to solve the above-mentioned system. The using of CG method with suitable preconditioners causes clustering eigenvalues of the new system around 1. As a result, the stability and convergence rate are guaranteed and at most we reach the answer in a steps.

This paper proposes a novel hybrid conjugate gradient method for nonparametric statistical inference.The proposed method is a convex combination of the modified linear search (MLS) and Fletcher-Reeves (FR) methods, and it inherits the advantages of both methods. The FR method is known for its fast convergence, while the MLS method is known for its robustness to noise. The proposed method combines these advantages to achieve both fast convergence and robustness to noise. Our method is evaluated on a variety of nonparametric statistical problems, including kernel density estimation, regression, and classification. The results show that the new method outperforms the MLS and FR methods in terms of both accuracy and efficiency.