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Block-conjugate-gradient method
Physical Review D, 1989It is shown that by using the block-conjugate-gradient method several, say {ital s}, columns of the inverse Kogut-Susskind fermion matrix can be found simultaneously, in less time than it would take to run the standard conjugate-gradient algorithm {ital s} times. The method improves in efficiency relative to the standard conjugate-gradient algorithm as
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On the truncated conjugate gradient method
Mathematical Programming, 2000Trust region algorithms for the unconstrained optimization problem \(\min_{x\in\mathbb{R}^n} f(x)\), where the function \(f(x)\) is continuously differentiable, often need to solve the following subproblem \[ \min_{d\in\mathbb{R}^n} g^Td+ d^TBd/2\quad\text{subject to }\|d\|\leq \Delta, \] where \(\Delta> 0\) is a trust region bound, \(g\in \mathbb{R}^n\
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Numerische Mathematik, 1963
The CG-algorithm is an iterative method to solve linear systems $$Ax + b = 0$$ (1) where A is a symmetric and positive definite coefficient matrix of order n. The method has been described first by Stiefel and Hesteness [1, 2] and additional information is contained in [3] and [4]. The notations used here coincide partially with those used in
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The CG-algorithm is an iterative method to solve linear systems $$Ax + b = 0$$ (1) where A is a symmetric and positive definite coefficient matrix of order n. The method has been described first by Stiefel and Hesteness [1, 2] and additional information is contained in [3] and [4]. The notations used here coincide partially with those used in
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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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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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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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