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Block-conjugate-gradient method
Physical Review D, 1989It is shown that by using the block-conjugate-gradient method several, say {ital s}, columns of the inverse Kogut-Susskind fermion matrix can be found simultaneously, in less time than it would take to run the standard conjugate-gradient algorithm {ital s} times. The method improves in efficiency relative to the standard conjugate-gradient algorithm as
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Orderings for Parallel Conjugate Gradient Preconditioners
SIAM Journal on Scientific Computing, 1997Summary: The efficient solution of the linear system of equations \(Ax=b\) on parallel computers sometimes requires a reordering of the unknowns. We investigate the effects of various orderings on the rate of convergence and the computation rate of the preconditioned conjugate gradient method with SSOR as the preconditioner.
S. A. Stotland, James M. Ortega
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On the truncated conjugate gradient method
Mathematical Programming, 2000Trust region algorithms for the unconstrained optimization problem \(\min_{x\in\mathbb{R}^n} f(x)\), where the function \(f(x)\) is continuously differentiable, often need to solve the following subproblem \[ \min_{d\in\mathbb{R}^n} g^Td+ d^TBd/2\quad\text{subject to }\|d\|\leq \Delta, \] where \(\Delta> 0\) is a trust region bound, \(g\in \mathbb{R}^n\
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On Restart Procedures for the Conjugate Gradient Method
Numerical Algorithms, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu-Hong Dai, Li-Zhi Liao, Duan Li 0002
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New Hybrid Conjugate Gradient and Broyden–Fletcher–Goldfarb–Shanno Conjugate Gradient Methods
Journal of Optimization Theory and Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Predrag S. Stanimirovic +3 more
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Nonmonotone conjugate gradient methods for optimization
1994In this paper conjugate gradient methods with nonmonotone line search technique are introduced. This new line search technique is based on a relaxation of the strong Wolfe conditions and it allows to accept larger steps. The proposed conjugate gradient methods are still globally convergent and, at the same time, they should not suffer the propensity ...
LUCIDI, Stefano, ROMA, Massimo
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Conjugate Gradient in Noisy Photometric Stereo
2014<p>This paper discusses the problem of reconstructing the Lambertian surface from noisy three-light source Photometric Stereo. In the continuous image setting the shape recovery process is divided into two steps: an algebraic one (gradient computation) and analytical one (gradient integration).
Ryszard Kozera +1 more
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Optimizing a Parallel Conjugate Gradient Solver
SIAM Journal on Scientific Computing, 1998Interesting report about the tuning of a classical (symmetric) conjugate gradient code for sparse matrices. At first the matrix-vector multiplication is tuned for a single processor (type IBM RS/6000), then for a parallel computer Hitachi SR4300 with up to 32 processors. Significant improvements compared to the naive code are obtained.
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Conjugate Gradient Methods with Inexact Searches
Mathematics of Operations Research, 1978Conjugate gradient methods are iterative methods for finding the minimizer of a scalar function f(x) of a vector variable x which do not update an approximation to the inverse Hessian matrix. This paper examines the effects of inexact linear searches on the methods and shows how the traditional Fletcher-Reeves and Polak-Ribiere algorithm may be ...
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2020
The conjugate gradient method was published by Hestenes and Stiefel in 1952, as a direct method for solving linear systems. Today its main use is as an iterative method for solving large sparse linear systems. On a test problem we show that it performs as well as the SOR method with optimal acceleration parameter, and we do not have to estimate any ...
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The conjugate gradient method was published by Hestenes and Stiefel in 1952, as a direct method for solving linear systems. Today its main use is as an iterative method for solving large sparse linear systems. On a test problem we show that it performs as well as the SOR method with optimal acceleration parameter, and we do not have to estimate any ...
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