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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. ...##
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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. ...##
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Solving the symmetric tridiagonal eigenvalue problem on hypercubes

1993
*
Computers and Mathematics with Applications
*

Using the methods of bisection and inverse

doi:10.1016/0898-1221(93)90135-i
fatcat:3zkqh37eabdchktbypzyvjsyma
*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. ...##
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Solving the Symmetric Tridiagonal Eigenvalue Problem on the Hypercube

1990
*
SIAM Journal on Scientific and Statistical Computing
*

Acknowledgements The authors wish to thank Stan Eisenstat, Bill Gropp, Cleve Moler, and Dan Sorensen 39

doi:10.1137/0911013
fatcat:kmgcvcvcefcpdolq7ylq6dpd4a
*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,... ...##
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Parallelizing the QR Algorithm for the Unsymmetric Algebraic Eigenvalue Problem: Myths and Reality

1996
*
SIAM Journal on Scientific Computing
*

Over the last few years, it has been suggested that the popular QR

doi:10.1137/0917056
fatcat:uoiezqwnyfcdnj2g5thbsf4koi
*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. ...##
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Development of a mathematical subroutine library for Fujitsu vector parallel processors

1998
*
Proceedings of the 12th international conference on Supercomputing - ICS '98
*

The aim of the project is to produce a library of mathematical subroutines

doi:10.1145/277830.277837
dblp:conf/ics/BrentGHHKKMNOZN98
fatcat:5q34v3i7srcf7mzagpod5din3y
*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. ...##
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A hybrid GMRES/LS-arnoldi method to accelerate the parallel solution of linear systems

2006
*
Computers and Mathematics with Applications
*

All of the

doi:10.1016/j.camwa.2006.05.004
fatcat:jopxv65zvrbkpo3omfjpq47wr4
*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. ...##
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Parallel numerical linear algebra

1993
*
Acta Numerica
*

Then, we present direct and

doi:10.1017/s096249290000235x
fatcat:xjigmj6i65cspl53s3wahom7bm
*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. ...##
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Solving Eigenvalue Problems on Networks of Processors
[chapter]

1999
*
Lecture Notes in Computer Science
*

The conclusion is that the solution of

doi:10.1007/10703040_8
fatcat:rwfczle2gjdizo655yz7rlpcne
*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*. ...##
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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. ...##
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Parallel Jacobi methods for derivative-free optimization on parallel or distributed processors

2005
*
ANZIAM Journal
*

New Jacobi-type

doi:10.21914/anziamj.v46i0.986
fatcat:5ufidapxibgexho7o4yyimq344
*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*. ...##
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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 ...##
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A Parallel Eigensolver for Dense Symmetric Matrices Based on Multiple Relatively Robust Representations

2005
*
SIAM Journal on Scientific Computing
*

We present a new

doi:10.1137/030601107
fatcat:w56ohdtiang3dow5ham2cshm6u
*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. ...##
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A RIGOROUS ANALYSIS OF TIME DOMAIN PARALLELISM∗

1995
*
Parallel Algorithms and Applications
*

Usually, the entire process is spatially

doi:10.1080/10637199508915498
fatcat:gfsbrey7ffhjrcqa6i5crfeuxu
*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*. ...##
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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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