A Parallel Method for Tridiagonal Equations
TL;DR: A new (partition) method for solving a tndiagonal system of lmear equations is presented and various situations under which the partmon method can be preferable are described.
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Abstract: 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. Although the partition method has a shghtly higher vector operatmn count than those of the two competing methods (the recursive doubling method and the cychc reduction method), it has a scalar count much smaller than that of the recursive doubling. The scalar counts between the partition method and the cyclic reduction method are so close as to make a timing evaluation inconclusive without considering the data management problem, especmlly when large systems are solved. Various situations under which the partmon method can be preferable are described.
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Citations
•Book
Solution of Partial Differential Equations on Vector and Parallel Computers
James M. Ortega,Robert G. Voigt +1 more
- 01 Jan 1987
TL;DR: The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms.
Parallel algorithms for dense linear algebra computations
TL;DR: The purpose is to review the current status and to provide an overall perspective of parallel algorithms for solving dense, banded, or block-structured problems arising in the major areas of direct solution of linear systems, least squares computations, eigenvalue and singular value computation, and rapid elliptic solvers.
214
Solving tridiagonal systems on ensemble architectures
TL;DR: Partitioning the ensemble into subsets of processors is shown to be more efficient for the solution of multiple independent problems than pipelining the solutions over the entire ensemble.
135
Developments and trends in the parallel solution of linear systems
Iain S. Duff,Henk A. van der Vorst +1 more
- 01 Dec 1999
TL;DR: This review paper considers some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism and considers preconditioning techniques for iterative solvers.
•Journal Article
Developments and trends in the parallel solution of linear systems
Iain S. Duff,HA van der Vorst +1 more
TL;DR: In this article, the authors consider some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism and discuss some of the present research issues in this field.
109
References
Parallel Tridiagonal Equation Solvers
TL;DR: Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations, and cyclic odd-even reduction appears to be the most preferable algorithm for all cases.
A Fast Computer Method for Matrix Transposing
TL;DR: A method is given for transposition of 2n×2n data matrices, larger than available high-speed storage, that should be stored on an external storage device, allowing direct access.
158
The Solution of Tridiagonal Linear Systems on the CDC STAR 100 Computer
TL;DR: The problem of solving tridmgonal linear systems on vector computers is considered and implementations of several direct and lterative methods are given for the Control Data Corporatlon STAR-100 computer.
140