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BLOCK PRECONDITIONING FOR THE CONJUGATE GRADIENT METHOD. APPENDIX

, 1982
Concus, P., Golub, G.H., Meurant, G.
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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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Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method

SIAM Journal on Scientific Computing, 2001
Summary: We describe new algorithms of the locally optimal block preconditioned conjugate gradient (LOBPCG) method for symmetric eigenvalue problems, based on a local optimization of a three-term recurrence, and suggest several other new methods. To be able to compare numerically different methods in the class, with different preconditioners, we ...
Andrew V Knyazev
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Ordering Methods for Preconditioned Conjugate Gradient Methods Applied to Unstructured Grid Problems

SIAM Journal on Matrix Analysis and Applications, 1992
The authors study the influence of various ordering techniques on the quality of the incomplete LU factorization used in the conjugate gradient method as preconditioner. They develop an ordering technique ( minimum discarded fill ordering) that is especially suited for finite element equations on unstructured grids. Applications to anisotropic problems
D'Azevedo, E. F., Forsyth, P. A., Tang, Wei-Pai   +2 more
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Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods

SIAM Journal on Scientific and Statistical Computing, 1981
The preconditioned conjugate gradient (PCG) method is an effective means for solving systems of linear equations where the coefficient matrix is symmetric and positive definite. The incomplete $LDL^t $ factorizations are a widely used class of preconditionings, including the SSOR, Dupont-Kendall-Rachford, generalized SSOR, ICCG(0), and MICCG(0 ...
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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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