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Other Conjugate Gradient Methods
2020As already seen, the conjugate gradient algorithms presented so far use some principles based on: hybridization or modifications of the standard schemes, the memoryless or the scaled memoryless BFGS preconditioned or the three-term concept. The corresponding conjugate gradient algorithms are defined by the descent condition, the “pure” conjugacy or the
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A conjugate gradient iterative method
Computers & Fluids, 1981Abstract A strongly implicit pre-conditioned form of the conjugate gradient method is considered. The resulting iterative technique is applicable for sparse systems of difference equations arising from boundary value problems. The method is used to solve two- and three-dimensional potential flows. In addition, it is extended to a 2 x 2 coupled system
P.K. Khosla, S.G. Rubin
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Standard Conjugate Gradient Methods
2020The purpose of this chapter is to present the standard conjugate gradient algorithms as well as their convergence for solving unconstrained optimization problems.
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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 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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Accelerated conjugate gradient method
An accelerated conjugate gradient method for the solution of operator equations is proposed. The convergence of the method is proved, its convergence rate is investigated, and results from numerical experiments are discussed. Also, a scheme for parallel computations is proposed.Luchka, A. Yu. +3 more
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