Methods of conjugate gradients for solving linear systems

By M. Hestenes, E. Stiefel. 1952

Subfields: Numerical Methods & Scientific Computing

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In Numerical Methods & Scientific Computing

Citations in the corpus

Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation (2019, methodology): “We use automatic differentiation and truncated conjugate gradient (Hestenes and Stiefel, 1952) to develop a “Hessian-free” implementation of R-SSN that allows computing the Newton update without additional memory overhead.”
Distributed optimization with arbitrary local solvers (2015, methodology): “CD Coordinate Descent [51] APPROX Accelerated, Parallel and Proximal Coordinate Descent [20, 21] GD Gradient Descent with Backtracking Line Search [44] CG Conjugate Gradient Method [25] L-BFGS Quasi-Newton with Limited-Memory BFGS Updating [10] BB Barzilai-Borwein Gradient Method [4] FISTA Fast Iter”
Entropy Search for Information-Efficient Global Optimization (2011, methodology): “…for such settings include quasi-Newton methods (Broyden et al., 1965; Fletcher, 1970; Goldfarb, 1970; Shanno, 1970), the conjugate gradient method (Hestenes and Stiefel, 1952), and stochastic optimization and evolutionary search methods (e.g. Hansen and Ostermeier (2001)), to name only a few.”
Stochastic, Distributed and Federated Optimization for Machine Learning (2017, methodology): “CD Coordinate Descent [148] APPROX Accelerated, Parallel and Proximal Coordinate Descent [59] GD Gradient Descent with Backtracking Line Search [134] CG Conjugate Gradient Method [77] L-BFGS Quasi-Newton with Limited-Memory BFGS Updating [27] BB Barzilai-Borwein Gradient Method [9] FISTA Fast Iterat”
Reviving and Improving Recurrent Back-Propagation (2018, methodology): “(9) in the derivation of original RBP, one would naturally think of the most common iterative solver, i.e., conjugate gradient method (Hestenes & Stiefel, 1952).”
Sourcebook of parallel computing (2003, methodology): “This was the original conjugate gradient method [467].”
Efficiently controlling for case-control imbalance and sample relatedness in large-scale genetic association studies (2017, methodology): “To further evaluate the computational performance of SAIGE, we randomly sampled subsets from the 408,458 white British UK Biobank participants who are defined as either coronary artery disease (CAD) cases (31,355) or controls (377,103) based on the PheWAS Code 411(3,32,33) followed by benchmarking a”
Modulation of electronic and mechanical properties of phosphorene through strain (2014, methodology): “Apart from the package used, calculations begin with the determination of the optimized geometry [29], i.”
PyCUDA and PyOpenCL: A scripting-based approach to GPU run-time code generation (2009, methodology): “Based on this feature, in turn, we were able to include a fast conjugate-gradient-based [16] linear system solver, which uses the GPU to solve large systems about ten times faster than competing CPU implementations.”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “1) by a Krylov subspace method such as GMRES (Generalized Minimal RESidual method) (Saad and Schultz, 1986) or CG (Conjugate Gradient method) (Hestenes and Stiefel, 1952).”
Deep Learning and Its Applications in Biomedicine (2018, methodology): “In addition, conjugate gradient combines conjugacy and gradient descent in the update direction decision for parameters, efﬁciently avoiding the calculation of the inverse Hessian [4,35,36], while contrastive divergence is usually used in RBM model [89–91].”