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Conjugate gradients
"... We have not yet put the Burg method of PEF estimation on a helix. The first reason to do so is that the Burg method assures us a stable PEF. The second reason to do so is that the Burg method should be much faster than conjugate gradients. For data length ND and filter length NF, the PEF estimation ..."
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We have not yet put the Burg method of PEF estimation on a helix. The first reason to do so is that the Burg method assures us a stable PEF. The second reason to do so is that the Burg method should be much faster than conjugate gradients. For data length ND and filter length NF, the PEF estimation
A scaled conjugate gradient algorithm for fast supervised learning
 NEURAL NETWORKS
, 1993
"... A supervised learning algorithm (Scaled Conjugate Gradient, SCG) with superlinear convergence rate is introduced. The algorithm is based upon a class of optimization techniques well known in numerical analysis as the Conjugate Gradient Methods. SCG uses second order information from the neural netwo ..."
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Cited by 451 (0 self)
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A supervised learning algorithm (Scaled Conjugate Gradient, SCG) with superlinear convergence rate is introduced. The algorithm is based upon a class of optimization techniques well known in numerical analysis as the Conjugate Gradient Methods. SCG uses second order information from the neural
The Multiparameter Conjugate Gradient Algorithm
, 2001
"... The multiparameter conjugate gradient algorithm is a generalization of the conjugate gradient algorithm for the solution of systems of linear equations with a symmetric positive de nite matrix. Some algebraic properties of this algorithm are proved and its convergence is studied. 1 ..."
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Cited by 1 (0 self)
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The multiparameter conjugate gradient algorithm is a generalization of the conjugate gradient algorithm for the solution of systems of linear equations with a symmetric positive de nite matrix. Some algebraic properties of this algorithm are proved and its convergence is studied. 1
/ Differentiating the Method of Conjugate Gradients ∗
, 2013
"... The method of conjugate gradients (CG) is widely used for the iterative solution of large sparse systems of equations ..."
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The method of conjugate gradients (CG) is widely used for the iterative solution of large sparse systems of equations
Conjugate Gradient Methods for Toeplitz Systems
 SIAM Review
, 1996
"... In this expository paper, we survey some of the latest developments on using preconditioned conjugate gradient methods for solving Toeplitz systems. One of the main results is that the complexity of solving a large class of nbyn Toeplitz systems is reduced to O(n log n) operations as compared to O ..."
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Cited by 174 (40 self)
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In this expository paper, we survey some of the latest developments on using preconditioned conjugate gradient methods for solving Toeplitz systems. One of the main results is that the complexity of solving a large class of nbyn Toeplitz systems is reduced to O(n log n) operations as compared
Flexible conjugate gradients
 SIAM J. Sci. Comput
, 2000
"... Abstract. We analyze the conjugate gradient (CG) method with preconditioning slightly variable from one iteration to the next. To maintain the optimal convergence properties, we consider a variant proposed by Axelsson that performs an explicit orthogonalization of the search directions vectors. For ..."
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Cited by 64 (8 self)
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Abstract. We analyze the conjugate gradient (CG) method with preconditioning slightly variable from one iteration to the next. To maintain the optimal convergence properties, we consider a variant proposed by Axelsson that performs an explicit orthogonalization of the search directions vectors
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
 ACM Trans. Graph
, 2003
"... Permission to make digital/hard copy of part of all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given ..."
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Cited by 297 (3 self)
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Permission to make digital/hard copy of part of all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given that copying is by permission
3. Conjugate gradient method
"... • conjugate gradient method for linear equations • convergence analysis • conjugate gradient method as iterative method • nonlinear conjugate gradient method 31 Unconstrained quadratic minimization minimize f(x) = 1 2 xT Ax−b T x with A ∈ S n ++ • equivalent to solving Ax = b • residual r = b−Ax i ..."
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• conjugate gradient method for linear equations • convergence analysis • conjugate gradient method as iterative method • nonlinear conjugate gradient method 31 Unconstrained quadratic minimization minimize f(x) = 1 2 xT Ax−b T x with A ∈ S n ++ • equivalent to solving Ax = b • residual r = b
Block preconditioning for the conjugate gradient method
, 1982
"... Abstract. Block preconditionings for the conjugate gradient method are investigated for solving positive definite block tridiagonal systems of linear equations arising from discretization of boundary value problems for elliptic partial differential equations. The preconditionings rest on the use of ..."
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Cited by 102 (5 self)
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Abstract. Block preconditionings for the conjugate gradient method are investigated for solving positive definite block tridiagonal systems of linear equations arising from discretization of boundary value problems for elliptic partial differential equations. The preconditionings rest on the use
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