Modified Two-Point Stepsize Gradient Methods for Unconstrained Optimization
Computational Optimization and Applications
Relaxed Steepest Descent and Cauchy-Barzilai-Borwein Method
Computational Optimization and Applications
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
Computational Optimization and Applications
Nonmonotone Globalization Techniques for the Barzilai-Borwein Gradient Method
Computational Optimization and Applications
A New Gradient Method with an Optimal Stepsize Property
Computational Optimization and Applications
Gradient Methods with Adaptive Step-Sizes
Computational Optimization and Applications
Hybrid spectral gradient method for the unconstrained minimization problem
Journal of Global Optimization
Notes on the Dai-Yuan-Yuan modified spectral gradient method
Journal of Computational and Applied Mathematics
Iterative regularization algorithms for constrained image deblurring on graphics processors
Journal of Global Optimization
Gradient-Based Methods for Sparse Recovery
SIAM Journal on Imaging Sciences
Expert Systems with Applications: An International Journal
A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand
Computational Optimization and Applications
Smooth and adaptive gradient method with retards
Mathematical and Computer Modelling: An International Journal
The Chaotic Nature of Faster Gradient Descent Methods
Journal of Scientific Computing
Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging
SIAM Journal on Imaging Sciences
A Dynamical Tikhonov Regularization for Solving Ill-posed Linear Algebraic Systems
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Linear convergence analysis of the use of gradient projection methods on total variation problems
Computational Optimization and Applications
A globally optimal tri-vector method to solve an ill-posed linear system
Journal of Computational and Applied Mathematics
A control Liapunov function approach to generalized and regularized descent methods for zero finding
International Journal of Hybrid Intelligent Systems
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A generalization of the steepest descent and other methods for solving a large scale symmetric positive definitive system Ax = b is presented. Given a positive integer m, the new iteration is given by $x_{k+1} = x_k - \lambda (x_{\nu(k)}) (A x_k - b)$, where $\lambda (x_{\nu(k)})$ is the steepest descent step at a previous iteration $\nu(k) \in \{k, k-1, \ldots,$ max$\{0,k-m\}\}$. The global convergence to the solution of the problem is established under a more general framework, and numerical experiments are performed that suggest that some strategies for the choice of $\nu(k)$ give rise to efficient methods for obtaining approximate solutions of the system.