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NeuraLSP: An Efficient and Rigorous Neural Left Singular Subspace Preconditioner for Conjugate Gradient Methods [PDF]

Alexander Benanti, Xi Han, Hong Qin
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Vectorization of some block preconditioned conjugate gradient methods

Parallel Computing, 1990
Although the preconditioned conjugate gradient methods are effective for solving the linear systems arising from discretization of elliptic partial differential equations, the solution of the linear system \(Mr=s\), \(M=LD^{-1}L^ T\), where D, L are, respectively, diagonal and bidiagonal block matrices, to get the preconditioned residual, is a quite ...
BRUGNANO, LUIGI, M. MARRONE
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The Stochastic Preconditioned Conjugate Gradient method

Probabilistic Engineering Mechanics, 1992
Abstract This paper presents the Stochastic Preconditioned Conjugate Gradient method (SPCG), an iterative equation solver that can greatly reduce the computational effort associated with the repeated calculations required in probabilistic finite element analysis.
Robert H. Sues, Heh-Chyun Chen, Francis M. Lavelle   +2 more
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Preconditioned conjugate gradient methods for adaptive filtering

1991 IEEE International Symposium on Circuits and Systems (ISCAS), 1991
The method of preconditioned conjugate gradients (PCGs) is proposed for solving the problem of adaptive filtering. Considered as an iterative algorithm, the PCG algorithm is asymptotically efficient. It is suggested for use in applications requiring very high order adaptive filters.
A.W. Hull, W.K. Jenkins
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Image restoration with precondition conjugate gradient method

2014 7th International Congress on Image and Signal Processing, 2014
Image restoration can be attributed to solving a linear systems and conjugate gradient method is an effective iteration algorithm for solving various linear systems. However the convergence rate of CGM is determined by condition number of coefficient matrix.
Bin Zhang, Ling Meng
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Inexact Preconditioned Conjugate Gradient Method with Inner-Outer Iteration

SIAM Journal on Scientific Computing, 1999
An inexact preconditioned conjugate gradient algorithm is formulated for a symmetric positive definite system. A linear convergence result is established using a local relation of residual norms, and it is shown that the algorithm may have the superlinear convergence property when the inner iteration is solved to high accuracy.
Golub, Gene H., Ye, Qiang
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Stochastic Optimization Using the Stochastic Preconditioned Conjugate Gradient Method

AIAA Journal, 1996
The SPCG solver has been integrated into NIKE3D and used to conduct a Monte Carlo simulation and a stochastic shape optimization of a cantilever ...
Oakley, David R., Sues, Robert H.
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Preconditioning conjugate gradient method for nonsymmetric systems

International Journal of Computer Mathematics, 1995
It is well known that the preconditioned conjugate gradient algorithms (PCG) work very well (for both symmetric and nonsymmetric problems) if the preconditioned is “good enough”. But, in many cases, “good enough” means that for solving (during the application of (PCG)) the systems in which the preconditioning matrix appears too much computational work ...
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