Relevant bibliographies by topics / Preconditioned conjugate gradients

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Preconditioned conjugate gradients'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Preconditioned conjugate gradients"

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Wang, Weichung. "Final iterations in interior point methods – preconditioned conjugate gradients and modified search directions." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 41, no. 3 (2000): 312–28. http://dx.doi.org/10.1017/s0334270000011267.

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AbstractIn this article we consider modified search directions in the endgame of interior point methods for linear programming. In this stage, the normal equations determining the search directions become ill-conditioned. The modified search directions are computed by solving perturbed systems in which the systems may be solved efficiently by the preconditioned conjugate gradient solver. A variation of Cholesky factorization is presented for computing a better preconditioner when the normal equations are ill-conditioned. These ideas have been implemented successfully and the numerical results show that the algorithms enhance the performance of the preconditioned conjugate gradients-based interior point methods.
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Strakoš, Zdeněk, and Petr Tichý. "Error Estimation in Preconditioned Conjugate Gradients." BIT Numerical Mathematics 45, no. 4 (2005): 789–817. http://dx.doi.org/10.1007/s10543-005-0032-1.

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Wolkowicz, Henry. "Solving semidefinite programs using preconditioned conjugate gradients." Optimization Methods and Software 19, no. 6 (2004): 653–72. http://dx.doi.org/10.1080/1055678042000193162.

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Kaasschieter, E. F. "Preconditioned conjugate gradients for solving singular systems." Journal of Computational and Applied Mathematics 24, no. 1-2 (1988): 265–75. http://dx.doi.org/10.1016/0377-0427(88)90358-5.

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Duff, Iain S., and Gérard A. Meurant. "The effect of ordering on preconditioned conjugate gradients." BIT 29, no. 4 (1989): 635–57. http://dx.doi.org/10.1007/bf01932738.

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Collignon, Tijmen, and Martin Van Gijzen. "Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids." International Journal of Applied Mathematics and Computer Science 20, no. 1 (2010): 109–21. http://dx.doi.org/10.2478/v10006-010-0008-4.

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Two implementations of the preconditioned conjugate gradient method on heterogeneous computing gridsEfficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify the various bottlenecks induced by the middleware and the iterative algorithm. We consider the standard CG algorithm of Hestenes and Stiefel, and as an alternative the Chronopoulos/Gear variant, a formulation that is potentially better suited for grid computing since it requires only one synchronisation point per iteration, instead of two for standard CG. In addition, we improve the computation-to-communication ratio by maximising the work in the preconditioner. In addition to these algorithmic improvements, we also try to minimise the communication overhead within the communication model currently used by the GridSolve middleware. We present numerical experiments on 3D bubbly flow problems using heterogeneous computing hardware that show lower computing times and better speed-up for the Chronopoulos/Gear variant of conjugate gradients. Finally, we suggest extensions to both the iterative algorithm and the middleware for improving granularity.
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Baxter, B. J. C. "Preconditioned conjugate gradients, radial basis functions, and Toeplitz matrices." Computers & Mathematics with Applications 43, no. 3-5 (2002): 305–18. http://dx.doi.org/10.1016/s0898-1221(01)00288-7.

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Manero, O. "Finite difference solution of viscoelastic flows by preconditioned conjugate gradients." Numerical Methods for Partial Differential Equations 2, no. 4 (1986): 317–26. http://dx.doi.org/10.1002/num.1690020406.

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Pilkington, Mark. "3-D magnetic imaging using conjugate gradients." GEOPHYSICS 62, no. 4 (1997): 1132–42. http://dx.doi.org/10.1190/1.1444214.

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A 3-D inversion approach is outlined that determines a distribution of susceptibility that produces a given magnetic anomaly. The subsurface model consists of a 3-D array of rectangular blocks, each with a constant susceptibility. The inversion incorporates a model norm that allows smoothing and depth‐weighting of the solution. Since the number of parameters can be many thousands, even for small problems, the linear system of equations is inverted using a preconditioned conjugate gradient approach. This reduces memory requirements and avoids large matrix multiplications. The method is used to determine the 3-D susceptibility distribution responsible for the Temagami magnetic anomaly in southern Ontario, Canada.
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Pini, G., G. Gambolati, and G. Galeati. "3-D finite element transport models by upwind preconditioned conjugate gradients." Advances in Water Resources 12, no. 2 (1989): 54–58. http://dx.doi.org/10.1016/0309-1708(89)90001-8.

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Dissertations / Theses on the topic "Preconditioned conjugate gradients"

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Al-Jeiroudi, Ghussoun. "On inexact Newton directions in interior point methods for linear optimization." Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/3863.

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In each iteration of the interior point method (IPM) at least one linear system has to be solved. The main computational effort of IPMs consists in the computation of these linear systems. Solving the corresponding linear systems with a direct method becomes very expensive for large scale problems. In this thesis, we have been concerned with using an iterative method for solving the reduced KKT systems arising in IPMs for linear programming. The augmented system form of this linear system has a number of advantages, notably a higher degree of sparsity than the normal equations form. We design a block triangular preconditioner for this system which is constructed by using a nonsingular basis matrix identified from an estimate of the optimal partition in the linear program. We use the preconditioned conjugate gradients (PCG) method to solve the augmented system. Although the augmented system is indefinite, short recurrence iterative methods such as PCG can be applied to indefinite system in certain situations. This approach has been implemented within the HOPDM interior point solver. The KKT system is solved approximately. Therefore, it becomes necessary to study the convergence of IPM for this inexact case. We present the convergence analysis of the inexact infeasible path-following algorithm, prove the global convergence of this method and provide complexity analysis.
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Ajmani, Kumud. "Preconditioned conjugate gradient methods for the Navier-Stokes equations." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39840.

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A generalized Conjugate Gradient like method is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. Preconditioning techniques are employed with the Conjugate Gradient like method to enhance the stability and convergence rate of the overall iterative method. The superiority of the new solver is established by comparisons with a conventional Line GaussSeidel Relaxation (LGSR) solver. Comparisons are based on 'number of iterations required to converge to a steady-state solution' and 'total CPU time required for convergence'. Three test cases representing widely varying flow physics are chosen to investigate the performance of the solvers. Computational test results for very low speed (incompressible flow over a backward facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (shockon- shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the 1vfach 0.1 case, speed-up factors of 30 (in terms of iterations) and 20 (in terms of CPU time) are found in favor of the new solver when compared with the LGSR solver. The corresponding speed-up factors for the transonic flow case are 20 and 18, respectively. The hypersonic case shows relatively lower speed-up factors of 5 and 4, respectively. This study reveals that preconditioning can greatly enhance the range of applicability and improve the performance of Conjugate Gradient like methods.<br>Ph. D.
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Michaud-Rioux, Vincent. "Real space DFT by locally optimal block preconditioned conjugate gradient method." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110628.

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In condensed matter physics, atomistic first principle calculations are often necessary to achieve a microscopic understanding of the observed experimental phenomena and to make quantitative predictions of physical properties. In practice, atomic scale systems have irregularities (e.g. surface roughness) or defects (e.g. substitutional atoms or vacancies) that are too strong to be ignored or treated as small perturbations. In this thesis, we report the development of a real space DFT code for studying atomic scale systems from first principles. Our code, named MatRcal, which stands for "Matlab-based real space calculator", is developed in the technical computing language Matlab. The physics is described by density functional theory. The method itself is based on projecting the Kohn-Sham Hamiltonian on a uniform Cartesian grid. High-order finite-differencing is used to discretize the Laplacian operator. The potential due to the atomic nuclei is approximated with ab initio pseudopotentials. The pseudopotentials are generated following the procedure proposed by Troullier and Martins. We use the fully separable form introduced by Kleinman and Bylander. We argue that the method is simpler and yet has many advantages compared with conventional spectral methods. We provide relevant mathematical techniques and implementation details. In particular, we present and compare different eigensolvers used to diagonalize the Kohn-Sham Hamiltonian. We validate our software by comparing the HOMO-LUMO gaps of many organic and inorganic molecules obtained using our method with those obtained with the commercial code Gaussian. Our results are in excellent agreement. Our method gains in computational speed and algorithm parallelism, and its power in handling real space boundary conditions will be a major advantage for future applications in nanoelectronic device modelling.<br>En physique de la matière condensée, les calculs numériques sont souvent nécessaires pour parvenir à comprendre les phénomènes microscopiques observés lors d'expériences ou à prédire quantitativement des propriétés physiques. En pratique, les systèmes d'échelle atomique sont irréguliers (rugosité de surface) ou comportent des défauts (atomes de substitution ou lacunes), ce qui induit des effets trop sévères pour être ignorés ou traités comme des perturbations. Dans cette thèse, nous présentons une méthode qui permet d'étudier des systèmes d'échelle atomique à partir des lois fondamentales de la physique. Notre logiciel, nommé MatRcal, qui signifie "Matlab-based real space calculator", est développé dans le langage Matlab. La physique est décrite par la théorie de la fonctionnelle de la densité. La méthode projette l'Hamiltonien de Kohn-Sham sur un maillage Cartésien uniforme. Le calcul des différences finies est utilisé pour discrétiser l'opérateur Laplacien. Le potentiel dû aux noyaux atomiques est approximé par des pseudopotentiels non-empiriques. Les pseudopotentiels sont générés en suivant la procédure proposée par Troullier et Martins. Nous utilisons la forme séparable introduite par Kleinman et Bylander. Nous soutenons que la méthode est plus simple et pourtant présente de nombreux avantages par rapport aux conventionnelles méthodes spectrales. Nous introduisons plusieurs techniques mathématiques pertinentes à notre étude et certains détails d'implémentation. Entre autres, nous présentons et comparons plusieurs algorithmes de calcul de vecteurs propres utilisés pour diagonaliser l'Hamiltonien de Kohn-Sham. Nous validons notre méthode en comparant la largeur de bande interdite "HOMO-LUMO" de nombreuses molécules organiques et inorganiques prédites par notre méthode avec celles prédites par le logiciel commercial Gaussian. Notre méthode permet des gains en rapidité et en parallélisme, mais la possibilité de traiter des conditions limites non-périodiques sera le principal atout pour de futures simulations de dispositifs nanoélectroniques.
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Irani, Kashmira M. "Preconditioned sequential and parallel conjugate gradient algorithms for homotopy curve tracking." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/41971.

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<p>There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Variants of the conjugate gradient algorithm along with different preconditioners are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. In addition, a parallel version of Craig's method with incomplete LU factorization preconditioning is implemented on a shared memory parallel computer with various levels and degrees of parallelism (e.g., linear algebra, function and Jacobian matrix evaluation, etc.). An in-depth study is presented for each of these levels with respect to the speedup in execution time obtained with the parallelism, the time spent implementing the parallel code and the extra memory allocated by the parallel algorithm.<br>Master of Science
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Gupta, Radhika. "Support graph preconditioners for sparse linear systems." Thesis, Texas A&M University, 2004. http://hdl.handle.net/1969.1/1353.

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Elliptic partial differential equations that are used to model physical phenomena give rise to large sparse linear systems. Such systems can be symmetric positive definite and can be solved by the preconditioned conjugate gradients method. In this thesis, we develop support graph preconditioners for symmetric positive definite matrices that arise from the finite element discretization of elliptic partial differential equations. An object oriented code is developed for the construction, integration and application of these preconditioners. Experimental results show that the advantages of support graph preconditioners are retained in the proposed extension to the finite element matrices.
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Pester, M., and S. Rjasanow. "A parallel version of the preconditioned conjugate gradient method for boundary element equations." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800455.

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The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.
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Solov'ëv, Sergey I. "Preconditioned iterative methods for monotone nonlinear eigenvalue problems." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600657.

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This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue problem, we suggest preconditioned iterative methods: preconditioned simple iteration method, preconditioned steepest descent method, and preconditioned conjugate gradient method. These methods use only matrix-vector multiplications, preconditioner-vector multiplications, linear operations with vectors and inner products of vectors. We investigate the convergence and derive grid-independent error estimates of these methods for computing eigenvalues. Numerical experiments demonstrate practical effectiveness of the proposed methods for a class of mechanical problems.
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O'Neal, Jerome W. "The use of preconditioned iterative linear solvers in interior-point methods and related topics." Diss., Available online, Georgia Institute of Technology, 2005, 2005. http://etd.gatech.edu/theses/available/etd-06242005-162854/.

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Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2006.<br>Parker, R. Gary, Committee Member ; Shapiro, Alexander, Committee Member ; Nemirovski, Arkadi, Committee Member ; Green, William, Committee Member ; Monteiro, Renato, Committee Chair.
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金小慶 and Xiao-qing Jin. "Circulant preconditioners for Toeplitz matrices and their applicationsin solving partial differential equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1992. http://hub.hku.hk/bib/B31232607.

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Matthes, H. "Parallel Preconditioners for Plate Problem." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800826.

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This paper concerns the solution of plate bending problems in domains composed of rectangles. Domain decomposition (DD) is the basic tool used for both the parallelization of the conjugate gradient method and the construction of efficient parallel preconditioners. A so-called Dirich- let DD preconditioner for systems of linear equations arising from the fi- nite element approximation by non-conforming Adini elements is derived. It is based on the non-overlapping DD, a multilevel preconditioner for the Schur-complement and a fast, almost direct solution method for the Dirichlet problem in rectangular domains based on fast Fourier transform. Making use of Xu's theory of the auxiliary space method we construct an optimal preconditioner for plate problems discretized by conforming Bogner-Fox-Schmidt rectangles. Results of numerical experiments carried out on a multiprocessor sys- tem are given. For the test problems considered the number of iterations is bounded independent of the mesh sizes and independent of the number of subdomains. The resulting parallel preconditioned conjugate gradient method requiresO(h^-2 ln h^-1 ln epsilon^-11) arithmetical operations per processor in order to solve the finite element equations with the relative accuracy epsilon.
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Books on the topic "Preconditioned conjugate gradients"

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Axelsson, Owe, and Lily Yu Kolotilina, eds. Preconditioned Conjugate Gradient Methods. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0090897.

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Lai, C. H. Preconditioned conjugate gradient methods on the DAP. Queen Mary College, Department of Computer Science and Statistics, 1987.

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Pan, Victor. A fast, preconditioned conjugate gradient Toeplitz solver. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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Freund, Roland W. On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices. Research Institute for Advanced Computer Science, 1989.

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Hill, Mary Catherine. Preconditioned Conjugate-Gradient 2 (PCG2), a computer program for solving ground-water flow equations. Dept. of the Interior, U.S. Geological Survey, 1990.

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Hill, Mary Catherine. Preconditioned Conjugate-Gradient 2 (PCG2), a computer program for solving ground-water flow equations. Dept. of the Interior, U.S. Geological Survey, 1990.

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Hill, Mary Catherine. Preconditioned Conjugate-Gradient 2 (PCG2), a computer program for solving ground-water flow equations. Dept. of the Interior, U.S. Geological Survey, 1990.

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Hill, Mary Catherine. Preconditioned Conjugate-Gradient 2 (PCG2), a computer program for solving ground-water flow equations. Dept. of the Interior, U.S. Geological Survey, 1990.

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Hill, Mary Catherine. Preconditioned Conjugate-Gradient 2 (PCG2), a computer program for solving ground-water flow equations. Dept. of the Interior, U.S. Geological Survey, 1990.

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T, Chronopoulos A. Implementation of preconditioned S-step conjugate gradient methods on a multiprocessor system with memory hierarchy. Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1987.

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Book chapters on the topic "Preconditioned conjugate gradients"

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Cook, Rod. "Preconditioned Conjugate Gradients on the PUMA Architecture." In Scientific Computing on Supercomputers III. Springer US, 1992. http://dx.doi.org/10.1007/978-1-4899-2581-7_3.

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Zlatev, Zahari. "Preconditioned Conjugate Gradients for Givens Plane Rotations." In Computational Methods for General Sparse Matrices. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-017-1116-6_16.

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Galeati, Giorgio, Giorgio Pini, and Giuseppe Gambolati. "Upwind Preconditioned Conjugate Gradients for Finite Element Transport Models." In Groundwater Contamination: Use of Models in Decision-Making. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2301-0_27.

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Shan, Xiujie, and Martin van Gijzen. "Deflated Preconditioned Conjugate Gradients for Nonlinear Diffusion Image Enhancement." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55874-1_45.

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Andrei, Neculai. "Conjugate Gradient Methods Memoryless BFGS Preconditioned." In Nonlinear Conjugate Gradient Methods for Unconstrained Optimization. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42950-8_8.

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Accary, Gilbert, Oleg Bessonov, Dominique Fougère, Konstantin Gavrilov, Sofiane Meradji, and Dominique Morvan. "Efficient Parallelization of the Preconditioned Conjugate Gradient Method." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03275-2_7.

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Yuk, Jacky Shun-Cho, and Kwan-Yee Kenneth Wong. "Adaptive Background Defogging with Foreground Decremental Preconditioned Conjugate Gradient." In Computer Vision – ACCV 2012. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37447-0_46.

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Crone, Lianne G. C. "The preconditioned conjugate gradient method on distributed memory systems." In High-Performance Computing and Networking. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-57981-8_114.

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Fillmore, Travis B., Varun Gupta, and Carlos Armando Duarte. "Preconditioned Conjugate Gradient Solvers for the Generalized Finite Element Method." In Meshfree Methods for Partial Differential Equations IX. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15119-5_1.

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Gupta, Rohit, Martin B. van Gijzen, and Cornelis Kees Vuik. "Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38718-0_7.

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Conference papers on the topic "Preconditioned conjugate gradients"

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Dellaert, F., J. Carlson, V. Ila, Kai Ni, and C. E. Thorpe. "Subgraph-preconditioned conjugate gradients for large scale SLAM." In 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010). IEEE, 2010. http://dx.doi.org/10.1109/iros.2010.5650422.

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De Stefano, Michele, Federico Golfré Andreasi, and Alberto Secchi. "Towards preconditioned nonlinear conjugate gradients for generic geophysical inversions." In SEG Technical Program Expanded Abstracts 2013. Society of Exploration Geophysicists, 2013. http://dx.doi.org/10.1190/segam2013-0244.1.

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Kushida, Noriyuki, Hiroshi Okuda, and Genki Yagawa. "Large-Scale Parallel Finite Element Analysis of the Stress Singular Problems." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22562.

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In this paper, the convergence behavior of large-scale parallel finite element method for the stress singular problems was investigated. The convergence behavior of iterative solvers depends on the efficiency of the preconditioners. However, efficiency of preconditioners may be influenced by the domain decomposition that is necessary for parallel FEM. In this study the following results were obtained: Conjugate gradient method without preconditioning and the diagonal scaling preconditioned conjugate gradient method were not influenced by the domain decomposition as expected. symmetric successive over relaxation method preconditioned conjugate gradient method converged 6% faster as maximum if the stress singular area was contained in one sub-domain.
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Duan, Xifa, and Lv Quanyi. "The Construction of Parallel Preconditioner in Preconditioned Conjugate Gradient Method." In 2010 Second Global Congress on Intelligent Systems (GCIS). IEEE, 2010. http://dx.doi.org/10.1109/gcis.2010.173.

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Wang, Jianguo, and Guoyan Meng. "SAOR Preconditioned Conjugate Gradient Method." In Workshop on Intelligent Information Technology Application (IITA 2007). IEEE, 2007. http://dx.doi.org/10.1109/iita.2007.88.

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Pytlak, R., and T. Tarnawski. "Preconditioned conjugate gradient algorithms for nonconvex problems." In 2004 43rd IEEE Conference on Decision and Control (CDC). IEEE, 2004. http://dx.doi.org/10.1109/cdc.2004.4608810.

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Pytlak, R. "Preconditioned conjugate gradient algorithms with column scaling." In 2008 47th IEEE Conference on Decision and Control. IEEE, 2008. http://dx.doi.org/10.1109/cdc.2008.4738948.

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Eller, Paul R., and William Gropp. "Scalable Non-blocking Preconditioned Conjugate Gradient Methods." In SC16: International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE, 2016. http://dx.doi.org/10.1109/sc.2016.17.

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Yang, Changjiang, Ramani Duraiswami, and Larry S. Davis. "Super-resolution using preconditioned conjugate gradient method." In Second International Conference on Image and Graphics, edited by Wei Sui. SPIE, 2002. http://dx.doi.org/10.1117/12.477201.

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Yue, Xiaoqiang, Shi Shu, and Chunsheng Feng. "UA-AMG Methods for 2-D 1-T Radiation Diffusion Equations and Their CPU-GPU Implementations." In 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icone21-16157.

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In this paper, we study several unsmoothed aggregation based algebraic multigrid (UA-AMG) methods with regard to different characteristics of CPUs and graphics processing units (GPUs). We propose some UA-AMG methods with lower computational complexity for CPU and CPU-GPU, and study these UA-AMG methods mixing with 4 kinds of red-black colored Gauss-Seidel smoothers for CPU-GPU since the initial mesh is structured. These UA-AMG methods are used as preconditioners for the conjugate gradient (CG) solver to solve a class of two-dimensional single-temperature radiation diffusion equations discretized by preserving symmetry finite volume element scheme. Numerical results demonstrate that, UA-NA-CG-s, which wins the best robustness and efficiency among them, is much more efficient than the default AMG preconditioned CG solvers in HYPRE, AGMG and Cusp for CPU; Under CPU-GPU, UA-W-CG-p is the most robust and efficient one, and rather more efficient than the smoothed aggregation based AMG preconditioned CG solver in Cusp.
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Reports on the topic "Preconditioned conjugate gradients"

1

Moridis, G., K. Pruess, and E. Antunez. T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/145291.

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2

Kincaid, D., T. Oppe, and W. Joubert. An overview of NSPCG: A nonsymmetric preconditioned conjugate gradient package. Office of Scientific and Technical Information (OSTI), 1988. http://dx.doi.org/10.2172/6756232.

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3

Oppe, T., W. Joubert, and D. Kincaid. NSPCG (Nonsymmetric Preconditioned Conjugate Gradient) user's guide: Version 1. 0: A package for solving large sparse linear systems by various iterative methods. Office of Scientific and Technical Information (OSTI), 1988. http://dx.doi.org/10.2172/7035748.

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4

PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations. US Geological Survey, 1990. http://dx.doi.org/10.3133/wri904048.

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5

Computer program for solving ground-water flow equations by the preconditioned conjugate gradient method. US Geological Survey, 1987. http://dx.doi.org/10.3133/wri874091.

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