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Dai-Kou type conjugate gradient methods with a line search only using gradient [PDF]
Journal of Inequalities and Applications, 2017 In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope.
Yuanyuan Huang, Changhe Liu
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Conjugate Gradient Methods for Toeplitz Systems [PDF]
SIAM Review, 1996 The use of preconditioned conjugate gradient methods to solve linear systems of equations with Toeplitz matrices is discussed. Using this iterative method, the complexity is reduced from \(O(n\log^2n)\) operations for fast direct Toeplitz solvers to \(O(n \log n)\).
Raymond H Chan, Michael K Ng
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Nonlinear conjugate gradient methods in micromagnetics
AIP Advances, 2017 Conjugate gradient methods for energy minimization in micromagnetics are compared. The comparison of analytic results with numerical simulation shows that standard conjugate gradient method may fail to produce correct results. A method that restricts the
J. Fischbacher +11 more
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A family of conjugate gradient methods for large-scale nonlinear equations [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved.
Dexiang Feng, Min Sun, Xueyong Wang
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Preconditioned conjugate gradient methods for absolute value equations
Journal of Numerical Analysis and Approximation Theory, 2020 We investigate the NP-hard absolute value equations (AVE), \(Ax-B|x| =b\), where \(A,B\) are given symmetric matrices in \(\mathbb{R}^{n\times n}, \ b\in \mathbb{R}^{n}\).
Nassima Anane, Mohamed Achache
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A NEW THREE -TERM CONJUGATE GRADIENT ALGORITHM FOR SOLVING MINIMIZATION PROBLEMS
Science Journal of University of Zakho, 2023 The method of optimization is used to determine the most precise value for certain functions within a certain domain; it is mostly studied and employed in the fields of mathematics, computer science, and physics.
Dilovan H. Omar +2 more
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A Combined Conjugate Gradient Quasi-Newton Method with Modification BFGS Formula
International Journal of Analysis and Applications, 2023 The conjugate gradient and Quasi-Newton methods have advantages and drawbacks, as although quasi-Newton algorithm has more rapid convergence than conjugate gradient, they require more storage compared to conjugate gradient algorithms.
Mardeen Sh. Taher, Salah G. Shareef
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Differentiating the Method of Conjugate Gradients [PDF]
SIAM Journal on Matrix Analysis and Applications, 2014 The method of conjugate gradients (CG) is widely used for the iterative solution of large sparse systems of equations $Ax=b$, where $A\in\Re^{n\times n}$ is symmetric positive definite. Let $x_k$ denote the $k$th iterate of CG. This is a nonlinear differentiable function of $b$. In this paper we obtain expressions for $J_k$, the Jacobian matrix of $x_k$
Serge Gratton +3 more
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EURO Journal on Computational Optimization, 2022 Nonlinear conjugate gradients are among the most popular techniques for solving continuous optimization problems. Although these schemes have long been studied from a global convergence standpoint, their worst-case complexity properties have yet to be ...
Rémi Chan–Renous-Legoubin +1 more
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Least-squares-based three-term conjugate gradient methods
Journal of Inequalities and Applications, 2020 In this paper, we first propose a new three-term conjugate gradient (CG) method, which is based on the least-squares technique, to determine the CG parameter, named LSTT.
Chunming Tang, Shuangyu Li, Zengru Cui
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