Results 21 to 30 of about 13,326,208 (288)
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
openaire +2 more sources
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
doaj +1 more source
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
openaire +2 more sources
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
doaj +1 more source
A New Spectral Conjugate Gradient method for solving unconstrained Optimization problems [PDF]
مجلة ابحاث كلية التربية الاساسية, 2022 The spectral conjugate gradient methods are fascinating, and it has been shown that they are useful for strictly convex quadratic reduction when used properly.
أسامة محمد طاهر ویس +2 more
doaj +1 more source
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.
openaire +3 more sources
Shape Optimization with Nonlinear Conjugate Gradient Methods
, 2023 In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce the methods as well as the corresponding theoretical background and investigate their performance ...
Blauth, Sebastian
core +1 more source
A Conjugate Gradient-Based BPTT-Like Optimal Control Algorithm With Vehicle Dynamics Control Application [PDF]
, 2010 The paper presents a gradient-based algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm has a backward-in-time recurrent structure similar to the backpropagation-through-time ...
Kolmanovsky, Ilya V. +10 more
core +1 more source
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
doaj +1 more source
Optimal CD-DY Conjugate Gradient Methods with Sufficient Descent [PDF]
المجلة العراقية للعلوم الاحصائية, 2013 Conjugate Gradient (CG) methods are widely used for large scale unconstrained optimization problems. Most of CG-methods don’t always generate a descent search direction, so the descent condition is usually assumed in the analysis and implementations.
Abbas Y. Al-Bayati, Hawraz N. Al-Khayat
doaj +1 more source