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A parallel algorithm for circulant tridiagonal linear systems

Yaw-Wen Chang, Chang-Biau Yang
1998 Information Processing Letters  
In this paper, based upon the divide-and-conquer strategy, we propose a parallel algorithm for solving the circulant tridiagonal systems, which is simpler than the two previous algorithms proposed by Agui  ...  Our algorithm can be easily generalized to solve the tridiagonal systems, the block-tridiagonal systems, and the circulant block-tridiagonal systems. @ 1998 Elsevier Science B.V.  ...  Agui and Jimenez [ 1 ] proposed a parallel algorithm to solve the tridiagonal systems. And, Chung et al. [4] proposed a parallel algorithm to solve the circulant block-tridiagonal systems.  ... 
doi:10.1016/s0020-0190(98)00018-0 fatcat:pzrjmyervnbl5iiq2geiz6vjcm

Parallel Tridiagonal Equation Solvers

Harold S. Stone
1975 ACM Transactions on Mathematical Software  
This paper compares three parallel algorithms for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC IV and CDC STAR.  ...  The quadratic convergence is superior to the linear convergence reported by Traub for several parallel iterative tridiagonal solvers. Parallel Tridiagonal Equation Solvers by Harold S. Stone  ...  Gene Golub of Stanford University for many discussions, comments, and suggestions regarding this paper. We also acknowledge helpful suggestions and conversations with Prof.  ... 
doi:10.1145/355656.355657 fatcat:dcegxoxuajhllhqsig6yz75ota

A recursive doubling algorithm for solution of tridiagonal systems on hypercube multiprocessors

Ömer Eǧecioǧlu, Cetin K. Koc, Alan J. Laub
1989 Journal of Computational and Applied Mathematics  
In this paper, we give a limited processor version of the recursive doubling algorithm for the solution of tridiagonal linear systems using O(n/p +log p) parallel arithmetic steps on a parallel computer  ...  The recursive doubling algorithm as developed by Stone can be used to solve a tridiagonal linear system of size n on a parallel computer with n processors using O(log n) parallel arithmetic steps.  ...  We are currently implementing parallel algorithms for the solutions of general recurrence relations, tridiagonal, block tridiagonal, and banded linear systems on the Intel hypercube, and investigating  ... 
doi:10.1016/0377-0427(89)90362-2 fatcat:kxuexu4sarftpfdodseo6b5gye

A Parallel Method for Tridiagonal Equations

H. H. Wang
1981 ACM Transactions on Mathematical Software  
A new (partition) method for solving a tndiagonal system of lmear equations is presented in this paper The method is suitable for both parallel and vector computers.  ...  smaller than that of the recursive doubling.  ...  They also gave conditions for stability of the recursive doubling algorithm as applied to the LU decomposition of a tridiagonal system.  ... 
doi:10.1145/355945.355947 fatcat:pf46qvc4nfgk3ma5vb6n5aw76i

An iteration-based hybrid parallel algorithm for tridiagonal systems of equations on multi-core architectures

Guangping Tang, Wangdong Yang, Kenli Li, Yu Ye, Guoqing Xiao, Keqin Li
2015 Concurrency and Computation  
The present paper will describe several parallel tridiagonal solvers and present a new hybrid parallel algorithm for the tridiagonal systems.  ...  The Thomas algorithm, a specific Gaussian elimination method, is one of the first algorithms considered for tridiagonal linear system.  ...  Thanks are also due to Qinghong Yang and Yulu Pan for the discussions on efficient multithreading implementation of the parallel algorithms.  ... 
doi:10.1002/cpe.3511 fatcat:fcmtcrbwvrhrdnjaahoucjpztq

Toward an Efficient Parallel Eigensolver for Dense Symmetric Matrices

Bruce Hendrickson, Elizabeth Jessup, Christopher Smith
1998 SIAM Journal on Scientific Computing  
We describe a parallel algorithm for finding the eigenvalues and eigenvectors of a dense symmetric matrix.  ...  Since the different steps have different algorithmic characteristics, this problem serves as an perfect vehicle for exploring some issues associated with parallel linear algebra calculations, In particular  ...  llidiagonzdiza tion Algorithm. Our parallel algorithm for Householder tridiagonalization for processor q is depicted in Fig. 6 .  ... 
doi:10.1137/s1064827596300681 fatcat:xmdfnmoakzbh3kankiszjfxrom

Analysis of non-strict functional implementations of the Dongarra-Sorensen eigensolver

S. Sur, W. Böhm
1994 Proceedings of the 8th international conference on Supercomputing - ICS '94  
We study the producer-consumer parallelism of Eigensolvers composed of a tridiagonalization function, a tridiagonal solver, and a matrix multiplication, written in the non-strict functional programming  ...  We show that in a non-strict functional execution model, the Dongarra-Sorensen algorithm can run completely in parallel with the Householder function.  ...  For the tridiagonal solver we h a v e studied implementations of the Dongarra-Sorensen algorithm and compared them with the more traditional QL algorithm.  ... 
doi:10.1145/181181.181574 dblp:conf/ics/SurB94 fatcat:742uwp2fvjhhzgk25bs4lathsq

A time-optimal algorithm for solving (block-)tridiagonal linear systems of dimension N on a distributed computer of N nodes [article]

Martin Neuenhofen
2018 arXiv   pre-print
Our paper presents two major results: First, we provide an algorithm that achieves the optimal parallel time complexity for solving a tridiagonal linear system and thin-banded linear systems.  ...  We are concerned with the fastest possible direct numerical solution algorithm for a thin-banded or tridiagonal linear system of dimension N on a distributed computing network of N nodes that is connected  ...  Conclusions We presented an algorithm for the efficient parallel solution of (block-)tridiagonal linear systems.  ... 
arXiv:1801.09840v2 fatcat:pgync2sfandk7eslvrh6u3y6d4

Generalized scans and tridiagonal systems

Paul F. Fischer, Franco P. Preparata, John E. Savage
2001 Theoretical Computer Science  
We also describe a variety of parallel algorithms including some that are well known for tridiagonal systems and some that are much better suited to distributed computation.  ...  Motivated by the analysis of known parallel techniques for the solution of linear tridiagonal system, we i n troduce generalized scans, a class of recursively de ned lengthpreserving, sequence-to-sequence  ...  for its bearing on the solution of banded systems naturally viewed as block tridiagonal systems.  ... 
doi:10.1016/s0304-3975(99)00311-4 fatcat:4t3vu2u4wngelbkejjtbyc654i

Implementation of parallel tridiagonal solvers for a heterogeneous computing environment

Hamish J Macintosh, David J Warne, Neil A Kelson, Jasmine E Banks, Troy W Farrell
2016 ANZIAM Journal  
Algorithms such as cyclic reduction and spike reduce a single large tridiagonal system into multiple small independent systems which are solved in parallel.  ...  The standard Thomas algorithm for solving such systems is inherently serial, forming a bottleneck in computation.  ...  A special thanks to the hpc group for their support, particularly in providing access to specialist fpga and gpu resources.  ... 
doi:10.21914/anziamj.v56i0.9371 fatcat:orvz7rja4jdvjkdbyu7ymx3e7e

Using cyclic reduction on a parallel computer to improve the performance of an underwater sound implicit finite difference model

Marilyn Santiago, David R. Kincaid
1991 Computers and Mathematics with Applications  
The numerical algorithm used in subroutine lrid of the IFD code, for solving a tridiagonal system of equations is based on Gaussian elimination and is recursive.  ...  The cyclic reduction algorithm of Hockney and Jesshope [10] is an algorithm for solving tridiagonal systems of equations that can be vectorized and that can utilize the unique characteristics of a parallel  ... 
doi:10.1016/0898-1221(91)90218-s fatcat:z2yrbeootrfjbb7ejxz52meaoe

Cluster Computation for Flood Simulations1 [chapter]

Ladislav Hluchy, Giang T. Nguyen, Ladislav Halada, Viet D. Tran
2001 Lecture Notes in Computer Science  
Simulation of the water flood problems often leads to solving of large sparse systems of partial differential equations. For such systems, the numerical method is very CPU-time consuming.  ...  Therefore, the parallel simulation is essential for water flood study with satisfactory accuracy.  ...  The cyclic reduction algorithm was chosen because of its possibility for parallelism and better computational runtime than the recursive doubling algorithm.  ... 
doi:10.1007/3-540-48228-8_43 fatcat:v7slsobodnblfeeizftl2nlvl4

Generalized scans and tri-diagonal systems [chapter]

Paul F. Fischer, Franco P. Preparata, John E. Savage
1995 Lecture Notes in Computer Science  
We also describe a variety of parallel algorithms including some that are well known for tridiagonal systems and some that are much better suited to distributed computation.  ...  Motivated by the analysis of known parallel techniques for the solution of linear tridiagonal system, we i n troduce generalized scans, a class of recursively de ned lengthpreserving, sequence-to-sequence  ...  tridiagonal system 6 with one less equation, to be solved formally via recursion, and a single equation for y 3 which is solved subsequently.  ... 
doi:10.1007/3-540-59042-0_71 fatcat:vdb23x2p5veh5op35oyt2s2voi

A PARALLEL PREFIX ALGORITHM FOR ALMOST TOEPLITZ TRIDIAGONAL SYSTEMS

XIAN-HE SUN, RONALD D. JOSLIN
1995 International journal of high speed computing  
Experimental results show that the simple parallel prex algorithm is a good algorithm for symmetric, almost symmetric Toeplitz tridiagonal systems and for the compact scheme on high-performance computers  ...  However, the resulting systems from compact schemes are tridiagonal systems that are dicult to solve eciently on parallel computers.  ...  Carter of the Scalable Computing Laboratory at Ames Laboratory for providing the access and general help on the Ames 16K PEs MarPar parallel computer.  ... 
doi:10.1142/s0129053395000300 fatcat:2ymegf55g5a6vpa7b75qxerjsm

Page 6012 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
The authors present an algebraic abstraction of various well- established techniques for parallel decomposition of tridiagonal systems of linear equations.  ...  There is no requirement that the recursion be applied by centering on each record in sequential order, allowing the approach to cover a wide variety of deflationary recursive algorithms amenable to parallel  ... 
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