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Oracle computations in parallel numerical linear algebra

B. Codenotti, M. Leoncini, G. Resta
1994 Theoretical Computer Science  
Resta, Oracle computations in parallel numerical linear algebra, Theoretical Computer Science 127 (1994) 99-121.  ...  Using a new notion of reducibility, we investigate, in a model of approximate parallel computation, the behaviour of several known reductions among important problems in linear algebra.  ...  , [2] on the relations between complexity and stability in algebraic computations).  ... 
doi:10.1016/0304-3975(94)90102-3 fatcat:t7xkrshnkjbarehakiukyibnqe

On Speed versus Accuracy: Some Case Studies

Mauro Leoncini
1996 Journal of Complexity  
parallel time, and (3) reductions among computational problems do not in general constitute a practical tool for solving numerical problems.  ...  We study the complexity of some computational problems in case certain stability guarantees are required.  ...  To compute the n values p( k ) we can invoke, in parallel, n copies of the oracle, that we assume take constant time.  ... 
doi:10.1006/jcom.1996.0016 fatcat:mss7vwdmivdlph7dcpphmfcegm

High Performance Optimization at the Door of the Exascale [article]

Claude Tadonki
2021 arXiv   pre-print
In fact, we always get a fraction of the technically available computing power (so-called theoretical peak), and the gap is likely to go hand-to-hand with the hardware complexity of the target system.  ...  interconnect for data exchanges among the computing nodes.  ...  We get a direct impact of parallel computing in numerical optimization through the advances in parallel numerical algebra [29, 52, 49] , with some of them being implemented into effective frameworks  ... 
arXiv:2106.11819v1 fatcat:7ggfr2dugnedth76v2tu7kajty

Self-Adapting Software for Numerical Linear Algebra Library Routines on Clusters [chapter]

Zizhong Chen, Jack Dongarra, Piotr Luszczek, Kenneth Roche
2003 Lecture Notes in Computer Science  
It has been developed in the framework of Self-Adapting Numerical Software (SANS) since we believe such an approach can deliver the convenience and ease of use of existing sequential environments bundled  ...  with the power and versatility of highly-tuned parallel codes that execute on clusters.  ...  We wish to thank the Ohio Supercomputing Center (OSC), the Computational Science and Mathematics Division at Oak Ridge National Laboratory (XTORC cluster), the Center for Computational Sciences at Oak  ... 
doi:10.1007/3-540-44863-2_65 fatcat:5omrddu5ujchbo3ggpprrchwou

Parallel algebraic reductions among numerical problems

B. Codenotti, M. Leoncini, G. Resta
1991 Applied Mathematics Letters  
In this note we consider, for a number of linear algebra problems, an environment allowing approximate computations.  ...  Motivated by this question, we present here some preliminary results on parallel reducibility within approximation settings which apply to a number of linear algebra problems. F be a field.  ...  INTRODUCTION The concept of resource bounded reduction has played a major role in deepening the understanding on the complexity of computational problems, in both combinatorial and algebraic settings.  ... 
doi:10.1016/0893-9659(91)90069-8 fatcat:intahc462jdrvim2k7mhl4xrcq

Gate-Level Simulation of Quantum Circuits [article]

George F. Viamontes, Manoj Rajagopalan, Igor L. Markov, John P. Hayes
2002 arXiv   pre-print
simulation in classical VLSI design.  ...  However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation.  ...  QuIDDs on the other hand present a middle-ground between real quantum computers and linear algebra simulation in terms of space complexity.  ... 
arXiv:quant-ph/0208003v1 fatcat:c3stjnybbvhupje6vxhadmxvpe

Page 256 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
85a:68053 inclusion of data sets, and it makes it possible to obtain a high degree of dynamic parallel computation for many applied programs encountered in practice.” Kolyada, S.  ...  Kutera, Ludék (CS-CHRL) 85a:68054 Erratum and addendum to: “Parallel computation and conflicts in memory access” [Inform. Process. Lett. 14 (1982), no. 2, 93-96; MR 83g:68038]. Inform. Process.  ... 

Numerical Study of the b-Ξ Flame Wrinkling Combustion Model in ORACLES Test Rig

Guilherme Henrique Santos, Wladimyr Dourado
2015 Journal of Aerospace Technology and Management  
However good industrial numerical combustion models need a practical requiring, in this way, a balance between speed and accuracy.  ...  A specially challenging experiment to test this combustion model is the ORACLES test rig whose two independent parallel inlet channels consistently influence the turbulent combustion, injecting fuel and  ...  reactive) Backward Euler Linear Upwind Algebraic 5 (reactive) Backward Euler Linear Upwind Transport table  ... 
doi:10.5028/jatm.v7i4.527 fatcat:egpbet7etfhdrctja7y7ws64pi

Page 1099 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
(I-CNR-EI; Pisa) Oracle computations in parallel numerical linear algebra. (English summary) Theoret. Comput. Sci. 127 (1994), no. 1, 99-121.  ...  The paper considers reductions between matrix problems such as computing the determinant, the characteristic polynomial, and the inverse and solving a system of linear equations with respect to parallel  ... 

Author Index Volume 127 (1994)

1994 Theoretical Computer Science  
Wood, Balance in AVL trees and space cost of brother trees (Fundamenfal Study) Codenotti, B., M. Leoncini and G. Resta, Oracle computations in parallel numerical linear algebra Coquide, J.-L., M.  ...  Sharma, Program size restrictions in computational learning Jantzen. M. and H. Petersen, Cancellation in context-free languages: enrichment by reduction Jeschke, C-D., see J.  ... 
doi:10.1016/0304-3975(94)90050-7 fatcat:zyznrn7m4nhgfofcltok6asss4

Index to Volumes 37 and 38

2004 Journal of symbolic computation  
Index to Volumes 37 and 38 Volume 37 A long note on Mulders' short product, 391 A parallel multi-modular algorithm for computing Lagrange resolvents, 547 A relative van Hoeij algorithm over number fields  ...  using a rational transform, 377 CLAUSEN, M. and MÜLLER, M., Generating fast Fourier transforms of solvable groups, 137 Computation of the finitistic dimension of monomial algebras, 537 Computing maximal  ...  -J., Parallel computation of determinants of matrices with polynomial entries, 749 MARTÍNEZ-MORO, E., Regular representations of finite-dimensional separable semisimple algebras and Gröbner bases, 575  ... 
doi:10.1016/s0747-7171(04)00109-9 fatcat:q3cckydpknhjhinygacsvlj52y

Page 1167 of Mathematical Reviews Vol. , Issue 84c [page]

1984 Mathematical Reviews  
polynomial number of oracle calls in any computation is also accepted relative to A by a nondeterministic oracle machine that simultaneously runs in polynomial time and uses linear work space.  ...  Bendix [Computational problems in abstract algebra (Oxford, 1967), 263-297, Pergamon, Oxford, 1970; MR 41 #134] an equivalent proper (minimal) complete system.  ... 

Page 1699 of Mathematical Reviews Vol. , Issue 86d [page]

1986 Mathematical Reviews  
Colbourn and Andrzej Proskurowski, Concurrent transmissions in broadcast networks (pp. 128-136); Max Croche- more, Linear searching for a square in a word (abstract) (p. 137); Peter Dybjer, Domain algebras  ...  COMPUTER SCIENCE 65W Parallel computation See also 65006, 65041, 65049, 65134, 65168. Konovalov, A. N.; Bugrov, A. N.; Elinov, V. D. Algorithms for parallelization of difference problems.  ... 

Performing Quantum Measurement in Suitably Entangled States Originates the Quantum Computation Speed Up [article]

Giuseppe Castagnoli, Dalida Monti, Alexander Sergienko
2000 arXiv   pre-print
Reaching state (11) with quantum parallel computation still requires one oracle run.  ...  linear in n.  ... 
arXiv:quant-ph/9908015v2 fatcat:ba4zwkbihzchvmgwibwn65ekxm

Page 3071 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
Positive and negative numerations of algebras. (Russian. Russian summary) Vychisl. Sistemy No. 139, Teor. Vychisl.  ...  Using the classes resulting by bounding resources in this parallel model, some separation results are finally obtained.  ... 
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