A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
A parallel algorithm for circulant tridiagonal linear systems
1998
Information Processing Letters
Preserved Fulltext
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
1975
ACM Transactions on Mathematical Software
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
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
1989
Journal of Computational and Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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
1981
ACM Transactions on Mathematical Software
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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
2015
Concurrency and Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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
1998
SIAM Journal on Scientific Computing
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
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
1994
Proceedings of the 8th international conference on Supercomputing - ICS '94
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2003; you can also visit the original URL.
The file type is application/pdf.
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]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
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
2001
Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2005; you can also visit the original URL.
The file type is application/pdf.
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
2016
ANZIAM Journal
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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
1991
Computers and Mathematics with Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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]
2001
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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]
1995
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2005; you can also visit the original URL.
The file type is application/pdf.
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
1995
International journal of high speed computing
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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 ...
« Previous
Showing results 1 — 15 out of 2,457 results