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A new smoothing modified three-term conjugate gradient method for l1 $l_{1}$-norm minimization problem [PDF]
Journal of Inequalities and Applications, 2018 We consider a kind of nonsmooth optimization problems with l1 $l_{1}$-norm minimization, which has many applications in compressed sensing, signal reconstruction, and the related engineering problems.
Shouqiang Du, Miao Chen
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A Combined Conjugate Gradient Quasi-Newton Method with Modification BFGS Formula [PDF]
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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A New Parameterized Conjugate Gradient Method based on Generalized Perry Conjugate Gradient Method
Tikrit Journal of Pure Science, 2023 A New Parameterized Conjugate Gradient Method based on Generalized Perry Conjugate Gradient Method is proposed to be based on Perry's idea, the descent condition and the global convergent is proven under Wolfe condition.
Khalil K. Abbo, Nazar K. Hussein
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Parallel conjugate gradient method
Lietuvos Matematikos Rinkinys, 2003 We investigate a parallel version of the preconditioned conjugate gradientmethod. A scalability analysis is done for a finite difference schemewhich approximates the 3D elliptic problem.
Raimondas Čiegis, Galina Šilko
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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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Comparison Between Steepest Descent Method and Conjugate Gradient Method by Using Matlab
Journal of Studies in Science and Engineering, 2021 The Steepest descent method and the Conjugate gradient method to minimize nonlinear functions have been studied in this work. Algorithms are presented and implemented in Matlab software for both methods.
Dana Taha Mohammed Salih +1 more
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A New Paired Spectral Gradient Method to Improve Unconstrained and Non-Linear Optimization [PDF]
Kirkuk Journal of Science, 2023 The conjugated spectral gradient (SCG) method is an effective method for non-constrained large-scale nonlinear optimization. In this work, a new spectral conjugate gradient method is proposed with a strong Wolfe-Powell line search (SWP). The new proposal
Siham Aziz, Zeyad Abdullah
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Anew Conjugate Gradient Algorithm Based on The (Dai-Liao) Conjugate Gradient Method
Tikrit Journal of Pure Science, 2020 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.
SHAHER QAHTAN HUSSEIN +2 more
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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 0001
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Block Preconditioning for the Conjugate Gradient Method [PDF]
SIAM Journal on Scientific and Statistical Computing, 1985 Different block preconditionings for the conjugate gradient methods are investigated for solving positive definite block tridiagonal systems. These preconditionings are based on different sparse approximate matrix inverses. The proposed methods are compared with other well-known preconditionings as for example the point incomplete Cholesky ...
Concus, P., Golub, G.H., Meurant, G.
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