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Page 78 of American Society of Civil Engineers. Collected Journals Vol. 9, Issue AS3 [page]

1996 American Society of Civil Engineers. Collected Journals  
This is significant in the light of highly iterative nature of the complex eigen- value problem. Speedups resulting from vectorization on a single processor for examples 3-6 are shown in Fig. 7.  ...  ‘‘A fully parallel algorithm for the symmetric eigenvalue problem.’’ SIAM J. Sci. Statist. Comput., 8(2), $139-S154. Dongarra, J.  ... 

Page 3813 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
Boley, Daniel (1-MN-C) 87g:65054 Solving the generalized eigenvalue problem on a synchronous linear processor array. Parallel Comput. 3 (1986), no. 2, 153-166.  ...  Summary: “We present a parallel method to solve the generalized eigenvalue problem on a linear array of processors, each connected to their nearest neighbors and operating synchronously.  ... 

Solving the symmetric tridiagonal eigenvalue problem on hypercubes

Kuo-Liang Chung, Wen-Ming Yan
1993 Computers and Mathematics with Applications  
Using the methods of bisection and inverse iteration respectively, this paper presents a parallel solver for the calculation of the eigenvalues of a real symmetric tridiagonal matrix on hypercube networks  ...  in O(ml logn) time using O(n2/logn) processors, where ml is the number of iterations.  ...  CONCLUDING REMARKS A parallel algorithm for solving the symmetric tridiagonal eigenvalues and eigenvectors problem has been presented.  ... 
doi:10.1016/0898-1221(93)90135-i fatcat:3zkqh37eabdchktbypzyvjsyma

Solving the Symmetric Tridiagonal Eigenvalue Problem on the Hypercube

Ilse C. F. Ipsen, Elizabeth R. Jessup
1990 SIAM Journal on Scientific and Statistical Computing  
Acknowledgements The authors wish to thank Stan Eisenstat, Bill Gropp, Cleve Moler, and Dan Sorensen 39 for many helpful discussions.  ...  An algorithm is implemented in parallel, in general, by dividing the work required into parts or tasks, some of which can be executed simultaneously.  ...  Algorithm MGS (m < p). In parallel, do on all processors j, 0 _ j < n -1 1. for k =0,...  ... 
doi:10.1137/0911013 fatcat:kmgcvcvcefcpdolq7ylq6dpd4a

Parallelizing the QR Algorithm for the Unsymmetric Algebraic Eigenvalue Problem: Myths and Reality

Greg Henry, Robert van de Geijn
1996 SIAM Journal on Scientific Computing  
Over the last few years, it has been suggested that the popular QR algorithm for the unsymmetric eigenvalue problem does not parallelize.  ...  In practice, reasonable speedup can be obtained on a MIMD distributed memory computer, for a relatively small number of processors.  ...  Our nal runs were made on Sandia's Paragon TM XP S Model 140 Supercomputer running SUNMOS S1.4.8, and we are grateful for this resource and operating system.  ... 
doi:10.1137/0917056 fatcat:uoiezqwnyfcdnj2g5thbsf4koi

Development of a mathematical subroutine library for Fujitsu vector parallel processors

R. Brent, B. Zhou, M. Nakanishi, L. Grosz, D. Harrar, M. Hegland, M. Kahn, G. Keating, G. Mercer, O. Nielsen, M. Osborne
1998 Proceedings of the 12th international conference on Supercomputing - ICS '98  
The aim of the project is to produce a library of mathematical subroutines for the vector-parallel Fujitsu VPP300 which result in high performance and accuracy on large problems.  ...  In order to utilise the architecture of the VPPSOO it is necessary to develop new algorithms for many of the standard numerical problems.  ...  Eigenvalue Problems The first algorithms developed for solving symmetric eigenvalue problems were based on the Jacobi method as this lends itself to parallel implementation.  ... 
doi:10.1145/277830.277837 dblp:conf/ics/BrentGHHKKMNOZN98 fatcat:5q34v3i7srcf7mzagpod5din3y

A hybrid GMRES/LS-arnoldi method to accelerate the parallel solution of linear systems

Haiwu He, G. Bergere, S. Petiton
2006 Computers and Mathematics with Applications  
All of the algorithms run on different processors of an IBM SP3 or IBM SP4 computer simultaneously.  ...  This method combines a parallel GMRES(m) algorithm with the least squares method that needs some eigenvalues obtained from a parallel Arnoldi algorithm.  ...  Perform simultaneously m' iterations of Arnoldi process on the other processors starting with to, and compute the eigenvalues of Sm,. 4.  ... 
doi:10.1016/j.camwa.2006.05.004 fatcat:jopxv65zvrbkpo3omfjpq47wr4

Parallel numerical linear algebra

James W. Demmel, Michael T. Heath, Henk A. van der Vorst
1993 Acta Numerica  
Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem, the nonsymmetric eigenvalue problem, the singular  ...  We rst discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing e cient algorithms.  ...  In the case of subspace iteration numerical instability m a y not be as severe as for the Lanczos process.  ... 
doi:10.1017/s096249290000235x fatcat:xjigmj6i65cspl53s3wahom7bm

Solving Eigenvalue Problems on Networks of Processors [chapter]

D. Giménez, C. Jiménez, M. J. Majado, N. Marín, A. Martín
1999 Lecture Notes in Computer Science  
The conclusion is that the solution of Eigenvalue Problems can be accelerated by using networks of processors and typical parallel algorithms, but the high cost of communications in these systems gives  ...  This is why it is interesting to study algorithms on networks of processors. In this paper we study on networks of processors different Eigenvalue Solvers.  ...  For these reasons, when designing algorithms for networks of processors it is preferable to think on good algorithms for a small number of processors, and not on scalable algorithms.  ... 
doi:10.1007/10703040_8 fatcat:rwfczle2gjdizo655yz7rlpcne

Page 385 of Mathematical Reviews Vol. , Issue 91A [page]

1991 Mathematical Reviews  
The resulting algorithms are implemented on a multiple instruc- tion multiple data grid architecture using 16 Transputer processors.  ...  (SGP-SING) An interactive method for the eigenvalue problem for matrices. Comput. Math. Appl. 19 (1990), no. 7, 43-51.  ... 

Parallel Jacobi methods for derivative-free optimization on parallel or distributed processors

I. D. Coope, M. S. Macklem
2005 ANZIAM Journal  
New Jacobi-type algorithms are presented for the efficient use of parallel and distributed computing platforms in solving derivativefree optimization problems.  ...  Convergence is usually achieved by introducing an elementary trust region sub-problem at synchronization steps in the algorithm.  ...  In Section 3 it is shown how parallel Jacobi methods for solving symmetric eigenvalue problems can also be exploited in unconstrained optimization algorithms.  ... 
doi:10.21914/anziamj.v46i0.986 fatcat:5ufidapxibgexho7o4yyimq344

Page 3761 of Mathematical Reviews Vol. , Issue 88g [page]

1988 Mathematical Reviews  
and the S-T algorithm for nonlinear eigenvalue problems.  ...  These are the algorithms: Rapido/Rapidissimo for linear systems, Bonaventura, Securitas and Velocitas for the linear eigen- value problem, the ECP algorithm for eigenvalue problems from damped vibrations  ... 

A Parallel Eigensolver for Dense Symmetric Matrices Based on Multiple Relatively Robust Representations

Paolo Bientinesi, Inderjit S. Dhillon, Robert A. van de Geijn
2005 SIAM Journal on Scientific Computing  
We present a new parallel algorithm for the dense symmetric eigenvalue/eigenvector problem that is based upon the tridiagonal eigensolver, Algorithm MR 3 , recently developed by Dhillon and Parlett.  ...  Algorithm MR 3 has a complexity of O(n 2 ) operations for computing all eigenvalues and eigenvectors of a symmetric tridiagonal problem.  ...  We are indebted to the Center for Computational Research at the University at Buffalo, SUNY, for the use of their 300 compute node Dell Linux Cluster.  ... 
doi:10.1137/030601107 fatcat:w56ohdtiang3dow5ham2cshm6u


1995 Parallel Algorithms and Applications  
Usually, the entire process is spatially parallelized by splitting the domain into subdomains and distributing problems on the subdomains to multiple processors see 3 and 5 .  ...  Starting from u 0 , which is known from the initial condition, we can use an iterative algorithm such as Jacobi, Gauss-Seidel, or SOR to solve 1 sequentially for each time step: u k i = T u k i , 1 +c;  ...  Consider an iterative s c heme for time domain parallelism by solving the linear systems at di erent time steps simultaneously.  ... 
doi:10.1080/10637199508915498 fatcat:gfsbrey7ffhjrcqa6i5crfeuxu

Page 5 of American Society of Civil Engineers. Collected Journals Vol. 13, Issue 1 [page]

2000 American Society of Civil Engineers. Collected Journals  
Saleh and Adeli (1996) present robust and efficient parallel algorithms for solution of the eigenvalue problem of an un- symmetric real matrix using the general approach of matrix iterations (Rutishauser  ...  In general, development of dis- tributed algorithms on a network of workstations is more chal- lenging than development of parallel algorithms on dedicated parallel machines as the distributed algorithm  ... 
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