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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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2019
Our interest in the conjugate gradient methods is twofold. First, they are among the most useful techniques to solve a large system of linear equations. Second, they can be adopted to solve large nonlinear optimization problems. In the previous chapters, we studied two important methods for finding a minimum point of real-valued functions of n real ...
Shashi Kant Mishra, Bhagwat Ram
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Our interest in the conjugate gradient methods is twofold. First, they are among the most useful techniques to solve a large system of linear equations. Second, they can be adopted to solve large nonlinear optimization problems. In the previous chapters, we studied two important methods for finding a minimum point of real-valued functions of n real ...
Shashi Kant Mishra, Bhagwat Ram
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The complex dynamic of conjugate gradient method
International Journal of Computer Mathematics, 2009Conjugate gradient method is a root-finding algorithm to non-linear equations. In this paper, we suggest extending this method for a polynomial to the complex plane. Through the experimental and theoretical mathematics method, we drew the following conclusions: (1) the conjugate gradient is a dynamical system with two complex parameters; (2) locally ...
Mohamed Lamine Sahari, Illhem Djellit
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2006
The endeavour to solve systems of linear algebraic systems is already two thousand years old. In the paper we consider the conjugate gradient method that is (theoretically) finite but, in practice, it can be treated as an iterative method. We survey a known modification of the method, the preconditioned conjugate gradient method, that may converge ...
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The endeavour to solve systems of linear algebraic systems is already two thousand years old. In the paper we consider the conjugate gradient method that is (theoretically) finite but, in practice, it can be treated as an iterative method. We survey a known modification of the method, the preconditioned conjugate gradient method, that may converge ...
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A modified PRP conjugate gradient method
Annals of Operations Research, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gonglin Yuan, Xiwen Lu
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Performance of the conjugate gradient method on Victor
Journal of Computational Physics, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Natarajan, Ramesh, Pattnaik, Pratap
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1994
In the following, A ∈ ℝ I x I and b ∈ ℝ I are real. We consider a system $$ Ax\, = \,b $$ (9.1.1) and assume that $$ A\,is\,positive\,definite. $$ (9.1.2) System (1) is associated with the function $$ F\left( x \right): = \,\frac{1}{2}\left\langle {Ax,\,x} \right\rangle \, - \,\left\langle {b,\,x} \right\rangle . $$ (9.1.3)
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In the following, A ∈ ℝ I x I and b ∈ ℝ I are real. We consider a system $$ Ax\, = \,b $$ (9.1.1) and assume that $$ A\,is\,positive\,definite. $$ (9.1.2) System (1) is associated with the function $$ F\left( x \right): = \,\frac{1}{2}\left\langle {Ax,\,x} \right\rangle \, - \,\left\langle {b,\,x} \right\rangle . $$ (9.1.3)
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Properties of generalized conjugate gradient methods
Numerical Linear Algebra with Applications, 1994AbstractThe solution of linear systems has considerable importance for the computation of problems resulting from engineering, physics, chemistry, computer science, mathematics, medicine and economics. The calculation of costly and time‐consuming problems, e.g. crash tests, simulation of the human lung and skin, calculation of electrical and magnetical
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Readily implementable conjugate gradient methods
Mathematical Programming, 1979Conjugate gradient methods have been extensively used to locate unconstrained minimum points of real-valued functions. At present, there are several readily implementable conjugate gradient algorithms that do not require exact line search and yet are shown to be superlinearly convergent. However, these existing algorithms usually require several trials
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