Cyclic reduction
Cyclic reduction is a numerical method for solving large linear systems by repeatedly splitting the problem. Each step eliminates even or odd rows and columns of a matrix and remains in a similar form. The elimination step is relatively expensive but splitting the problem allows parallel computation.

This is an excerpt from the article Cyclic reduction from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Cyclic reduction at en.wikipedia.org was accessed 175 times in the last 30 days. (as of: 11/21/2013)
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Cyclic reduction - Wikipedia, the free encyclopedia
Cyclic reduction is a numerical method for solving large linear systems by repeatedly splitting the problem. Each step eliminates even or odd rows and columns ...
en.wikipedia.org/wiki/Cyclic_reduction
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Cyclic Reduction – History and Applications - Department of ...
Abstract. We discuss the method of Cyclic reduction for solving special systems ... Cyclic reduction has proved to be an algorithm which is very powerful for.
www.inf.ethz.ch/personal/gander/papers/cyclic.pdf
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The cyclic reduction algorithm: from Poisson equation to stochastic ...
Abstract Cyclic reduction is an algorithm invented by G. H. Golub and R. W. ... survey the main features of Cyclic reduction, relate it to properties of analytic func- .
www.dm.unipi.it/~meini/papers/bm_cr09.pdf
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Cyclic Reduction - Stanford AI Lab - Stanford University
Nov 10, 1994 ... The method of Block Cyclic reduction BCR is described in the context of ... Cyclic reduction is a recursive, as opposed to iterative, algorithm ...
robotics.stanford.edu/~scohen/cr.pdf
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Remarks on the cyclic reduction method 1
time point of view, the Cyclic reduction method and an alternative, which uses recurrence relations, by using parallel calculus. 2000 Mathematics Subject ...
www.emis.de/journals/GM/vol18nr1/03_Chiorean/03_Chiorean.pdf
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Multicore parallelization of block cyclic reduction algorithm - Prace
Available online at www.prace-ri.eu. Partnership for Advanced Computing in Europe. Multicore parallelization of block Cyclic reduction algorithm. Dimitri Lecas a.
www.prace-ri.eu/IMG/pdf/multicoreparallelizationblockcyclicreduction.pdf
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The ordering of tridiagonal matrices in the cyclic reduction method ...
Our orderings are also applicable to the solution of Helmholtz's equation by Cyclic reduction, and to related numerical schemes, such as FACR methods.
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A Cyclic Reduction Algorithm for Solving Block Tridiagonal ... - JStor
Two algorithms of importance are the Buneman variant of Cyclic reduction ... continue the reduction scheme as above, we must introduce inverse matrices.
www.jstor.org/stable/2156489
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A parallel block cyclic reduction algorithm for the ... - ResearchGate
This paper presents an adaptation of the Block Cyclic reduction (BCR) ... into multiple scalar ones, or on using the general Block Cyclic reduction (BCR) as ...
www.researchgate.net/publication/220277338_A_parallel_block_cyclic_reduction_algorithm_for_the_fast_solution_of_elliptic_equations/file/e0b495151ba5147901.pdf
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CYCLIC_REDUCTION - A Direct Solution Method for Tridiagonal ...
May 11, 2010 ... CYCLIC_REDUCTION is a MATLAB library which applies the Cyclic reduction method to solve a tridiagonal system of linear equations A*x=b.
people.sc.fsu.edu/~%20jburkardt/m_src/cyclic_reduction/cyclic_reduction.html
Search results for "Cyclic reduction"
Cyclic reduction in science
[PDF]Cyclic Reduction – History and Applications - Department of ...
Cyclic reduction – History and Applications. Walter Gander and Gene H. Golub. ETH Zurich and Stanford University. Abstract. We discuss the method of Cyclic ...
[PDF]' Yale University Department of Computer Science
several variations of odd-even Cyclic reduction, and algorithms making use of data ... such as balanced Cyclic reduction, or a transpose based algorithm, may be ...
A parallel radix-4 block cyclic reduction algorithm - Myllykoski - 2013 ...
Sep 20, 2013 ... A conventional block Cyclic reduction algorithm operates by halving the size of the linear system at each reduction step, that is, the algorithm is ...
[PDF]A PARALLEL PARTIAL SOLUTION VARIANT OF CYCLIC ...
Damien Tromeur-Dervout, Nicolas Barberou, University of Claude Bernard. Lyon- 1, France ... Parallel partial fraction variant of Cyclic reduction [Sweet, 1988].
[PDF]Register Packing for Cyclic Reduction: A Case Study - IDAV
Mar 5, 2011 ... University of California, Davis aaldavidson@ucdavis.edu ... ply this generalization to Cyclic reduction, a tridiagonal solver with this pattern.
Cyclic reduction - Wikipedia, the free encyclopedia
Cyclic reduction is a numerical method for solving large linear systems by ... Art Of Scientific Computing p 885 ISBN 0-521-43108-5 Cambridge University Press  ...
A parallel block cyclic reduction algorithm for the fast solution of ...
A parallel block Cyclic reduction algorithm for the fast solution of elliptic equations (Report. University of Illinois at Urbana-Champaign. Center for ...
The ordering of tridiagonal matrices in the cyclic reduction method ...
The ordering of tridiagonal matrices in the Cyclic reduction method for ... Department of Mathematics, University of Kentucky, 40506, Lexington, KY, USA ...
Laboratory of Scienti c Computing, Department of Mathematics, University of Jyv ... The purpose of this paper is to develop a Cyclic reduction type formulation for ...
Books on the term Cyclic reduction
Numerical Recipes in Fortran 90: The Art of Parallel ...
1996
Cyclic reduction: Linear Recurrence Relations There is a variant of recursive doubling, called Cyclic reduction, that can be implemented with a straightforward iteration loop, instead of a recursive procedure call. [3] Here we start by writing ...
Multigrid
U. Trottenberg, Cornelis W. Oosterlee, Anton Schüller, 2001
This can be continued until after i — \ reduction steps a completely reduced system with a lower triangular matrix is ... Compared to other tridiagonal solvers, the Cyclic reduction method is distinguished by its particular numerical stability [ 343, ...
Proceedings of the Fifth SIAM Conference on Parallel ...
J. J. Dongarra, 1992
Repeatedly applying the Cyclic reduction algorithm continues to halve the bandwidth until all of the unresolved variables are calculated, at which time they can be injected into the next larger system to reduce its bandwidth. The Cyclic reduction ...
Reduction: Selectivity, Strategy & Efficiency in Modern Organic Chemistry
1992
This volume contains 37 chapters on methods for reducing functional groups, organized into four main parts. (i) Reduction of C=X systems, where X is an electronegative heteroatom, divided into 14 chapters based on the degree of reduction, the oxidation level of the C=X substrate, and on the nature of the reagent. (ii) Reduction of X=Y systems, divi...
Parallel Scientific Computing in C++ and MPI: A Seamless ...
For some matrices, the depth of reduction can be truncated because the solution can be obtained for one of the variables. ... PUTTING IT INTO PRACTICE We now present implementations of Cyclic reduction for tridiagonal systems. Owing to ...
Enhanced Oil Recovery Field Case Studies
2013
Enhanced Oil Recovery Field Case Studies bridges the gap between theory and practice in a range of real-world EOR settings. Areas covered include steam and polymer flooding, use of foam, in situ combustion, microorganisms, "smart water"-based EOR in carbonates and sandstones, and many more. Oil industry professionals know that the key to ...
Solution of Partial Differential Equations on Vector and ...
James M. Ortega, Robert G. Voigt, 1985
who considered an implementation of Cyclic reduction for the TI ASC, a computer which did not require that a vector be defined as elements in contiguous memory locations. Because of the overhead of data rearrangement, one would expect ...
Reductions by the Alumino- and Borohydrides in Organic Synthesis
1997
A complete guide to selection and use of the best reagents for a wide range of transformationsThis book is the updated and expanded Second Edition of Jacqueline Seyden-Penne's practical guide to selection of reducing reagents in organic synthesis. It is an indispensable working resource for organic synthetic chemists-the only reference focusin...

Blog posts on the term
Cyclic reduction
Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed Precision Multigrid :: GPGPU.org
Abstract: We have previously suggested mixed precision iterative solvers specifically tailored to the iterative solution of sparse linear equation systems as they typically arise in the finite element discretization of partial differential equations. These schemes have been evaluated for a number of hardware platforms, in particular single precision GPUs as accelerators to the general purpose CPU.
gpgpu.org/2010/03/03/cyclic-reduction-multigrid
Cyclic reduction algorithm and Buneman algorithm
Hello, I'm working with the equation Ax=B, where A is sparse, tridiagonal, symmetric and I want to solve it with the Cyclic reduction algorithm and
Multi-GPU Acceleration of Black-Scholes Equation based Option Pricing | hgpu.org
Multi-GPU Acceleration of Black-Scholes Equation based Option Pricing | Di Zhao, Jinhang Yu | Algorithms, CUDA, Differential equations, Finance, nVidia, nVidia GeForce GTX 660, Partial differential equations, PDEs
hgpu.org/?p=10577
See More Ar-15/M16/M-4 Rate Reducing Buffer – Carbine Rate Reducing Buffer | loplim.com
Steel rate-reducing buffer system slows down recoil two ways to improve accuracy and control. Extra weight lowers velocity for less wear on your bolt and receiver.
loplim.com/2013/12/31/See-More-Ar-15-M16-M-4-Rate-Reducing-Buffer-Carbine-Rate-Reducing-Buffer/
Obstetrics and Gynecology Publishes Data From Pivotal Phase 3 LYSTEDA Study - Drugs.com MedNews
First-ever, FDA-Approved Non-hormonal Treatment Option for Heavy Menstrual Bleeding PARSIPPANY, N.J., Ferring Pharmaceuticals Inc. today announced publication o
www.drugs.com/clinical_trials/obstetrics-gynecology-publishes-data-pivotal-phase-3-lysteda-study-10286.html
Arthritis Research & Therapy | Full text | Adalimumab clinical efficacy is associated with rheumatoid factor and anti-cyclic citrullinated peptide antibody titer reduction: a one-year prospective study
Studies on autoantibody production in patients treated with tumor necrosis factor-α (TNF-α) inhibitors reported contradictory results. We investigated in a prospective study the efficacy of a treatment with human monoclonal anti-TNF-α antibody (adalimumab) in patients with rheumatoid arthritis (RA) and we evaluated the relationship between treatment efficacy and the incidence and titers of disease-associated and non-organ-specific autoantibodies. Fifty-seven patients with RA not responsive to methotrexate and treated with adalimumab were enrolled. Antinuclear, anti-double-stranded(ds)DNA, anti-extractable nuclear antigens, anti-cardiolipin (aCL), anti-β2 glycoprotein I (anti-β2GPI) autoantibodies, rheumatoid factor (RF) and anti-cyclic citrullinated peptide (anti-CCP) autoantibodies were investigated at baseline and after 6 and 12 months of follow-up. Comparable parameters were evaluated in a further 55 patients treated with methotrexate only. Treatment with adalimumab induced a significant decrease in RF and anti-CCP serum levels, and the decrease in antibody titers correlated with the clinical response to the therapy. A significant induction of antinuclear autoantibodies (ANA) and IgG/IgM anti-dsDNA autoantibodies were also found in 28% and 14.6% patients, respectively, whereas aCL and anti-β2GPI autoantibodies were not detected in significant quantities. No association between ANA, anti-dsDNA, aCL and anti-β2GPI autoantibodies and clinical manifestations was found. Clinical efficacy of adalimumab is associated with the decrease in RF and anti-CCP serum levels that was detected after 24 weeks and remained stable until the 48th week of treatment. Antinuclear and anti-dsDNA autoantibodies, but not anti-phospholipid autoantibodies, can be induced by adalimumab but to a lower extent than in studies with other anti-TNF blocking agents.
arthritis-research.com/content/8/1/r3
Electrochemical Studies of Betti Base and Its Copper(II) Complex by Cyclic and Elimination Voltammetry
International Journal of Electrochemistry is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of electrochemistry.
www.hindawi.com/journals/ijelc/2013/678013/
Ar-15/M16/M-4 Rate Reducing Buffer – Carbine Rate Reducing Buffer Promo | Top.grsdc.net
Publish Date: 12/29/2013Category: UncategorizedThe Author: webmaster.
top.grsdc.net/2013/12/29/Ar-15-M16-M-4-Rate-Reducing-Buffer-Carbine-Rate-Reducing-Buffer-Promo/
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