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The constrained conjugate gradient algorithm
IEEE Signal Processing Letters, 2000Based on the condition for equivalence between linearly constrained minimum-variance (LCMV) filters and their generalized sidelobe canceler (GSC) implementations, we derive the new constrained conjugate gradient (CCG) algorithm. We discuss the use of orthogonal and nonorthogonal blocking matrices for the GSC structure and how the choice of this matrix ...
J. A. Apolinário Jr. +2 more
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Complex conjugate gradient methods
Numerical Algorithms, 1993The paper is concerned with the solution of linear systems with non- singular complex matrices. A unified framework is presented from which various conjugate gradient-like methods for solving the above described systems are derived. The considered methods include both well-known methods and some new variants of these methods.
Pascal Joly, Gérard Meurant
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Learning by conjugate gradients
1990A learning algorithm (CG) with superlinear convergence rate is introduced. The algorithm is based upon a class of optimization techniques well known in numerical analysis as the Conjugate Gradient Methods. CG uses second order information from the neural network but requires only O(N) memory usage, where N is the number of minimization variables; in ...
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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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Duality in conjugate gradient methods
Numerical Algorithms, 1999The authors present the reverse algorithms of \textit{Cs. J. Hegedüs} [Comput. Math. Appl. 21, No. 1, 71-85 (1991; Zbl 0727.65023)] in a new perspective and show how they are related to the more conventional algorithms if the latter is regarded as solving problems involving the original preconditioning matrices.
Broyden C. G., Foschi P.
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Conjugate Gradient Bundle Adjustment
2010Bundle adjustment for multi-view reconstruction is traditionally done using the Levenberg-Marquardt algorithm with a direct linear solver, which is computationally very expensive. An alternative to this approach is to apply the conjugate gradients algorithm in the inner loop.
Martin Byröd, Kalle Åström
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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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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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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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