Results 251 to 260 of about 781,590 (289)

Preconditioned conjugate gradient algorithms for nonconvex problems

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004
The paper describes a new conjugate gradient algorithm for large scale nonconvex problems. In order to speed up the convergence the algorithm employs a scaling matrix which transforms the space of original variables into the space in which Hessian matrices of functionals describing the problems have more clustered eigenvalues.
Radoslaw Pytlak, Tomasz Tarnawski
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Orderings for Conjugate Gradient Preconditionings

SIAM Journal on Optimization, 1991
The paper treats several ordering principles for the solution of Poisson- type elliptic boundary value problems with preconditioned conjugate gradient methods (PCG). As preconditioners SSOR and incomplete Cholesky (IC) are considered. For the solution of the relevant linear systems, which mostly are tridiagonal, on vector or parallel computers ...
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Preconditioned conjugate gradient method for generalized least squares problems [PDF]

Journal of Computational and Applied Mathematics, 1996
A variant of the preconditioned conjugate gradient method to solve generalized least squares problems is presented. If the problem is min (Ax − b)TW−1(Ax − b) with A ∈ Rm×n and W ∈ Rm×m symmetric and positive definite, the method needs only a ...
J.Y. Yuan, Iusem, A.N., A.N. Iusem, Yuan, J.Y.   +3 more
exaly   +2 more sources

Preconditioned conjugate gradient algorithms with column scaling

2008 47th IEEE Conference on Decision and Control, 2008
The paper describes new conjugate gradient algorithms which use preconditioning. The algorithms are intended for general nonlinear unconstrained problems. In order to speed up the convergence the algorithms employ scaling matrices which transform the space of original variables into the space in which Hessian matrices of functionals describing the ...
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On the Order of Convergence of Preconditioned Nonlinear Conjugate Gradient Methods

SIAM Journal on Scientific Computing, 1996
Summary: An analysis is given of preconditioned nonlinear conjugate gradient methods in which the preconditioning matrix is the exact Hessian matrix at each iteration (or a nearby matrix). It is shown that the order of convergence of certain preconditioned methods is less than of Newton's method when exact line searches are used, and an example is ...
Mehiddin Al-Baali, Robert Fletcher
openaire   +1 more source

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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Efficient Parallelization of the Preconditioned Conjugate Gradient Method

2009
In this paper we present methods for efficient parallelization of the solution of pressure Poisson equation arising in 3D CFD forest fire modeling. The solution procedure employs the Conjugate Gradient method with implicit Modified ILU (MILU) preconditioner.
Gilbert Accary, Oleg Bessonov, Dominique Fougère, Konstantin Gavrilov, Sofiane Meradji, Dominique Morvan   +5 more
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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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THE PRECONDITIONED CONJUGATE GRADIENT METHOD ON THE CONNECTION MACHINE

International Journal of High Speed Computing, 1989
This paper presents the results of the Connection Machine implementation of a number of preconditioners for the preconditioned conjugate gradient method. The preconditioners implemented include those based on the incomplete LU factorization, the modified incomplete LU factorization, the symmetric successive overrelaxation, and others such as several ...
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The effect of ordering on preconditioned conjugate gradients

BIT, 1989
The effect of ordering of the unknowns on the convergence of the preconditioned conjugate gradient method is investigated experimentally. 17 different orderings are studied on two model problems and two more complicated elliptic equations, using a modified version of the Yale sparse matrix package.
Duff, Iain S., Meurant, Gérard A.
openaire   +2 more sources