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Page 4721 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
The problem is solved by the preconditioned conjugate gradient method with preconditioners that can be inverted easily by using separation of variables.  ...  We recall the link with the second-order Richardson method and compare it with the conjugate gradient method.  ... 

Krylov Subspace Methods on Supercomputers

Youcef Saad
1989 SIAM Journal on Scientific and Statistical Computing  
Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three dimensional models gain importance.  ...  This paper presents a short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers.  ...  [51] and Adams and Ong [4] in the context of preconditioned conjugate gradient methods.  ... 
doi:10.1137/0910073 fatcat:owvjyuc5rrbzrjifjlaptljqku

Nonrecursive Order N formulation of multibody dynamics

ANDREW J. KURDILA, RAMESH G. MENON, JOHN W. SUNKEL
1993 Journal of Guidance Control and Dynamics  
Preconditioned Conjugate Gradient Solution The preconditioned conjugate gradient procedure is an ‘‘ac- celerated’’ variant of the classical conjugate gradient proce- dure.  ...  The method should be readily implementable on parallel processors since a vast literature exists on the amenability of the preconditioned conjugate gradient solution procedure to both concurrent and vector  ... 
doi:10.2514/3.21090 fatcat:xbfqm7k4efdpboo4fmbutqdkta

Page 1703 of American Society of Civil Engineers. Collected Journals Vol. 129, Issue 12 [page]

2003 American Society of Civil Engineers. Collected Journals  
Several other writers have studied the parallelization of the preconditioned conjugate gradient method in the context of the finite element method.  ...  Jordan and Hughes (1992) present algorithms for the implemen- tation of the finite element method for computational mechanics on Connection Machine systems.  ... 

Graph Cuts via $\ell_1$ Norm Minimization

A. Bhusnurmath, C.J. Taylor
2008 IEEE Transactions on Pattern Analysis and Machine Intelligence  
In this paper, the graph cut problem is reformulated as an unconstrained ' 1 norm minimization that can be solved effectively using interior point methods.  ...  This reformulation exposes connections between graph cuts and other related continuous optimization problems.  ...  [13] also describe how the preconditioned conjugate gradients method can be used to solve ' 1 regularized logistic regression problems.  ... 
doi:10.1109/tpami.2008.82 pmid:18703837 fatcat:wkngxrhvxnb3piylyvdxl76eze

Solving DWF Dirac Equation Using Multisplitting Preconditioned Conjugate Gradient [article]

Jiqun Tu
2018 arXiv   pre-print
We show that using the multisplitting algorithm as a preconditioner for conjugate gradient inversion of the domain wall fermion Dirac operator could effectively reduce the inter-node communication cost  ...  This method could be useful for supercomputers with far more on-node flops than inter-node communication bandwidth.  ...  We use the name MSPCG, as it is through the process of applying the multisplitting algorithm to the DWF Dirac equation that we realize the necessity of including the snake terms in the local matrix.  ... 
arXiv:1811.08488v1 fatcat:r5b62fvi65fyvdhjbwtymxcolq

On the performance of parallel normalized explicit preconditioned conjugate gradient type methods

G.A. Gravvanis, K.M. Giannoutakis
2006 Proceedings 20th IEEE International Parallel & Distributed Processing Symposium  
Parallel normalized explicit preconditioned conjugate gradient -type methods for distributed memory systems based on the block -row distribution (for the vectors and the explicit approximate inverse),  ...  A new class of parallel normalized preconditioned conjugate gradient type methods in conjunction with normalized approximate inverses algorithms, based on normalized approximate factorization procedures  ...  John Morrison of the Department of Computer Science, University College of Cork for proposing and allowing us to perform the test runs on the Departments' cluster.  ... 
doi:10.1109/ipdps.2006.1639612 dblp:conf/ipps/GravvanisG06 fatcat:xgpjihtncrex7amdfbrjx2x2ay

Page 257 of American Society of Civil Engineers. Collected Journals Vol. 119, Issue 3 [page]

1993 American Society of Civil Engineers. Collected Journals  
The assembled system of equations were solved in parallel using a conjugate gradient algorithm for unsymmetric, nonpositive definite systems. Numer- ical studies were done on connection machine 2.  ...  Carter et al. (1989) have proposed a parallel finite element program strategy using a parallel preconditioned-conjugate-gradient (PCG) solution procedure for substructuring analysis on MIMD multiprocessing  ... 

Some History of the Conjugate Gradient and Lanczos Algorithms: 1948–1976

Gene H. Golub, Dianne P. O'Leary
1989 SIAM Review  
CONJUGATE GRADIENT AND LANCZOS HISTORY 51 exploited; indeed, the method will converge in k or fewer iterations if the operator has k distinct eigenvalues.  ...  This paper gives some of the history of the conjugate gradient and Lanczos algorithms and an annotated bibliography for the period 1948-1976.  ...  "The Reproducing Kernel Method II," J. Math. Phys. Derives a connection between the conjugate gradient algorithm and the reproducing kernel method. 196. /CN/ Dixon, L.  ... 
doi:10.1137/1031003 fatcat:3xaapzhscfe3navaz2arpm76te

AN ITERATIVE SOLUTION METHOD FOR SCHUR COMPLEMENT SYSTEMS WITH INEXACT INNER SOLVER

OWE AXELSSON, MAYA NEYTCHEVA
1999 Recent Advances in Numerical Methods and Applications II  
In this paper, the Schur complement method with parallel preconditioned conjugate gradient (PCG) solver is introduced in two-dimensional parallel time-stepping finite element formulation to analyse rotating  ...  machine considering the electromagnetic field, external circuit and rotor movement.  ...  The used DDM is the Schur complement method with a parallel Krylov method, the parallel preconditioned conjugate gradient method [3] , which is currently one of the most popular methods for systems with  ... 
doi:10.1142/9789814291071_0081 fatcat:wuzfvhvwsnhrhpryrqpgmjyo44

The behavior of conjugate gradient algorithms on a multivector processor with a hierarchical memory

Ulrike Meier, Ahmed Sameh
1988 Journal of Computational and Applied Mathematics  
The algorithms considered consist of the classical conjugate gradient method, preconditioning techniques that are well suited for parallel computers such as polynomial preconditioners and several versions  ...  s, the analysis shows that conjugate gradient methods do not perform as well as algorithms for dense matrix computations on the considered architecture due to lack of data locality.  ...  Introduction Several studies [1, 3] have shown that, on sequential machines, the conjugate gradient method with preconditioning is one of the best methods for solving sparse symmetric positive definite  ... 
doi:10.1016/0377-0427(88)90341-x fatcat:h2sutev7yrezhnx5c6p2olptki

Highly Parallel Multigrid Solvers for Multicore and Manycore Processors [chapter]

Oleg Bessonov
2015 Lecture Notes in Computer Science  
In this paper we present an analysis of parallelization properties and implementation details of the new Algebraic multigrid solvers.  ...  This work was supported by the Russian Foundation for Basic Research (project RFBR-15-01-06363) and by the Institute of mathematics (IMATH) of the University of Toulon.  ...  Computations have been performed at the BULL's Computing Center, IMATH and Mésocentre of the University of Aix-Marseille, France.  ... 
doi:10.1007/978-3-319-21909-7_2 fatcat:sfknigej5rgddnr7zmkn54lfrm

Domain decomposition methods for large linearly elliptic three-dimensional problems

P.Le Tallec, Y.H.De Roeck, M. Vidrascu
1991 Journal of Computational and Applied Mathematics  
. / Domain decomposition methods niveau continu, la matrice complement de Schur au niveau discret) est ensuite inverse par un algorithme de gradient conjugue preconditionne.  ...  Sur cet exemple significatif, la methode proposee est competitive a la fois au niveau du temps calcul et de la place memoire.  ...  Conjugate gradient algorithm The solution of the interface problem (4) by a standard preconditioned conjugate gradient method, with preconditioner M, now leads to the following algorithm: Conjugate gradient  ... 
doi:10.1016/0377-0427(91)90150-i fatcat:eqrtxq2osbhsvjujyz3j7c7tz4

Page 381 of American Society of Civil Engineers. Collected Journals Vol. 123, Issue ST3 [page]

1997 American Society of Civil Engineers. Collected Journals  
‘“‘Comparison of preconditioned conjugate gradient method and LDL factorization for structural analysis.’’ Proc., /st Int. Conf. on Comp. and Information Technol. for Arch., Engrg., and Constr., H.  ...  *‘A data parallel finite element method for computational fluid dynam- ics on the connection machine system.’’ Comp. Methods in Appl. Mech. and Engrg., 99, 113-134. Johan, Z., Mathur, K.  ... 

High-performance conjugate-gradient benchmark: A new metric for ranking high-performance computing systems

Jack Dongarra, Michael A Heroux, Piotr Luszczek
2015 The international journal of high performance computing applications  
We describe a new high-performance conjugate-gradient (HPCG) benchmark. HPCG is composed of computations and data-access patterns commonly found in scientific applications.  ...  HPCG strives for a better correlation to existing codes from the computational science domain and to be representative of their performance.  ...  Acknowledgements The authors thank the Department of Energy National Nuclear Security Agency for the funding provided for this work.  ... 
doi:10.1177/1094342015593158 fatcat:dy7dmuxbwzdhrackranpeonjoq
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