scholarly journals Spectral CG Algorithm for Solving Fuzzy Nonlinear Equations

2022 ◽  
pp. 1-10
Author(s):  
Mezher M. Abed ◽  
Ufuk Öztürk ◽  
Hisham M. Khudhur
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Conjugacy Condition ◽  
Wide Range ◽  
Non Linear ◽  
Fuzzy Equations

The nonlinear conjugate gradient method is an effective technique for solving large-scale minimizations problems, and has a wide range of applications in various fields, such as mathematics, chemistry, physics, engineering and medicine. This study presents a novel spectral conjugate gradient algorithm (non-linear conjugate gradient algorithm), which is derived based on the Hisham–Khalil (KH) and Newton algorithms. Based on pure conjugacy condition The importance of this research lies in finding an appropriate method to solve all types of linear and non-linear fuzzy equations because the Buckley and Qu method is ineffective in solving fuzzy equations. Moreover, the conjugate gradient method does not need a Hessian matrix (second partial derivatives of functions) in the solution. The descent property of the proposed method is shown provided that the step size at meets the strong Wolfe conditions. In numerous circumstances, numerical results demonstrate that the proposed technique is more efficient than the Fletcher–Reeves and KH algorithms in solving fuzzy nonlinear equations.

scholarly journals A Modified Three-Term Type CD Conjugate Gradient Algorithm for Unconstrained Optimization Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhan Wang ◽  
Pengyuan Li ◽  
Xiangrong Li ◽  
Hongtruong Pham
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Trust Region ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
General Function ◽  
Term Type

Conjugate gradient methods are well-known methods which are widely applied in many practical fields. CD conjugate gradient method is one of the classical types. In this paper, a modified three-term type CD conjugate gradient algorithm is proposed. Some good features are presented as follows: (i) A modified three-term type CD conjugate gradient formula is presented. (ii) The given algorithm possesses sufficient descent property and trust region property. (iii) The algorithm has global convergence with the modified weak Wolfe–Powell (MWWP) line search technique and projection technique for general function. The new algorithm has made great progress in numerical experiments. It shows that the modified three-term type CD conjugate gradient method is more competitive than the classical CD conjugate gradient method.

scholarly journals New hybrid conjugate gradient method as a convex combination of FR and PRP methods

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3083-3100 ◽  
Author(s):  
Snezana Djordjevic
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Combination ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Numerical Comparisons ◽  
Hybrid Conjugate Gradient Method ◽  
Better Than

We consider a newhybrid conjugate gradient algorithm,which is obtained fromthe algorithmof Fletcher-Reeves, and the algorithmof Polak-Ribi?re-Polyak. Numerical comparisons show that the present hybrid conjugate gradient algorithm often behaves better than some known algorithms.

scholarly journals Conjugate gradient algorithm and fractals

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Mohamed Lamine Sahari ◽  
Ilhem Djellit
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Fractal Structures

This work is an extension of the survey on Cayley's problem in case where the conjugate gradient method is used. We show that for certain values of parameters, this method produces beautiful fractal structures.

Tomographic inversion via the conjugate gradient method

Geophysics ◽  
1987 ◽  
Vol 52 (2) ◽  
pp. 179-185 ◽  
Author(s):  
John A. Scales
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Sparse Matrices ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Algebraic Equations ◽  
Tomographic Inversion ◽  
Linear Algebraic Equations ◽  
The Matrix

Tomographic inversion of seismic traveltime residuals is now an established and widely used technique for imaging the Earth’s interior. This inversion procedure results in large, but sparse, rectangular systems of linear algebraic equations; in practice there may be tens or even hundreds of thousands of simultaneous equations. This paper applies the classic conjugate gradient algorithm of Hestenes and Stiefel to the least‐squares solution of large, sparse systems of traveltime equations. The conjugate gradient method is fast, accurate, and easily adapted to take advantage of the sparsity of the matrix. The techniques necessary for manipulating sparse matrices are outlined in the Appendix. In addition, the results of the conjugate gradient algorithm are compared to results from two of the more widely used tomographic inversion algorithms.

scholarly journals Anew Conjugate Gradient Algorithm Based on The (Dai-Liao) Conjugate Gradient Method

2020 ◽  
Vol 25 (1) ◽  
pp. 128
Author(s):  
SHAHER QAHTAN HUSSEIN1 ◽  
GHASSAN EZZULDDIN ARIF1 ◽  
YOKSAL ABDLL SATTAR2
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Numerical Results ◽  
Conjugate Gradient Algorithm ◽  
New Method ◽  
Gradient Algorithm ◽  
Search Direction ◽  
Descent Property

In this paper we can derive a new search direction of conjugating gradient method associated with (Dai-Liao method ) the new algorithm becomes converged by assuming some hypothesis. We are also able to prove the Descent property for the new method, numerical results showed for the proposed method is effective comparing with the (FR, HS and DY) methods.   http://dx.doi.org/10.25130/tjps.25.2020.019    

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