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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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properties of tridiagonal matrix inverses, can be computationally more efficient for the same computer storage than other preconditionings, including the popular point incomplete Cholesky factorization. Key words, conjugate gradient method, elliptic partial differential equations, incomplete factorization
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
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 653 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
Large steps in cloth simulation
 SIGGRAPH 98 Conference Proceedings
, 1998
"... The bottleneck in most cloth simulation systems is that time steps must be small to avoid numerical instability. This paper describes a cloth simulation system that can stably take large time steps. The simulation system couples a new technique for enforcing constraints on individual cloth particle ..."
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Cited by 576 (5 self)
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as well. The implicit integration method generates a large, unbanded sparse linear system at each time step which is solved using a modified conjugate gradient method that simultaneously enforces particles ’ constraints. The constraints are always maintained exactly, independent of the number of conjugate
The geometry of algorithms with orthogonality constraints
 SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
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Cited by 640 (1 self)
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In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2728 (61 self)
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successfully only because of recent advances in linear programming by interiorpoint methods. We obtain reasonable success with a primaldual logarithmic barrier method and conjugategradient solver.
Reconstruction and Representation of 3D Objects with Radial Basis Functions
 Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH
, 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
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Cited by 505 (1 self)
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We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs
A Flexible InnerOuter Preconditioned GMRES Algorithm
, 1993
"... We present a variant of the GMRES lgorithm which l]ows changes in the prcconditioning at every step. There arc many possible applications o the new lgorithm some o which arc briefly discussed. In particular, a result o the flexibility o the new variant is that any iterative method can bc used as a p ..."
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Cited by 358 (30 self)
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prcconditioncr. For example, the standard GMRES lgorithm itself can bc used as a prcconditioncr, as can CGNR (or CGNE) the conjugate gradient method applied to the normal equations. However, the more appealing utilization o the method is in conjunction with relaxation techniques, possibly multilevel techniques
SEMIDEFINITE PROGRAMMING RELAXATIONS FOR THE GRAPH PARTITIONING PROBLEM
, 1999
"... A new semidefinite programming, SDP, relaxation for the general graph partitioning problem, GP, is derived. The relaxation arises from the dual of the (homogenized) Lagrangian dual of an appropriate quadratic representation of GP. The quadratic representation includes a representation of the 0,1 co ..."
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Cited by 31 (6 self)
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dual interiorpoint solution technique. A gangster operator is the key to providing an efficient representation of the constraints in the relaxation. An incomplete preconditioned conjugate gradient method is used for solving the large linear systems which arise when finding the Newton direction. Only dual
Results 1  10
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