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Iterative method

About: Iterative method is a(n) research topic. Over the lifetime, 48860 publication(s) have been published within this topic receiving 1215121 citation(s). The topic is also known as: iterative method & iterative process. more


Journal ArticleDOI: 10.1016/0927-0256(96)00008-0
Georg Kresse1, Jürgen Furthmüller2Institutions (2)
Abstract: We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order Natoms2 scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special ‘preconditioning’ optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable. more

Topics: Projector augmented wave method (55%), Conjugate gradient method (55%), Iterative method (54%) more

40,008 Citations

Journal ArticleDOI: 10.1109/34.121791
Paul J. Besl1, H.D. McKay1Institutions (1)
Abstract: The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces. > more

Topics: Iterative closest point (63%), Point set registration (62%), Iterative method (55%) more

15,673 Citations

Open accessBook
01 Apr 2003-
Abstract: Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index. more

Topics: Krylov subspace (68%), Relaxation (iterative method) (67%), Multigrid method (65%) more

12,575 Citations

Open accessJournal ArticleDOI: 10.1137/0907058
Abstract: We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from t... more

10,155 Citations

Open accessProceedings ArticleDOI: 10.1117/12.965761
12 Nov 1981-
Abstract: Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image. more

Topics: Optical flow (59%), Horn–Schunck method (59%), Motion field (59%) more

8,045 Citations

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Topic's top 5 most impactful authors

Muhammad Aslam Noor

183 papers, 4.3K citations

Jumat Sulaiman

155 papers, 885 citations

Ioannis K. Argyros

135 papers, 1.1K citations

Juan R. Torregrosa

128 papers, 1.7K citations

Alicia Cordero

126 papers, 1.6K citations

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