Divide and conquer: A new parallel algorithm for the solution of a tridiagonal linear system of equations
We describe a divide and conquer algorithm which solves linear tridiagonal systems with one right-hand side, especially suited for parallel computers. The algorithm is very flexible, permits multiprocessing or a combination of vector and multiprocessor implementations, and is adaptable to a wide range of parallelism granularities. This algorithm can also be combined with recursive doubling, cyclic reduction or Wang's partition method, in order to increase the degree of parallelism and vectorizability.
The divide and conquer method will be explained. Some results of time measurements on a CRAY X-MP/28, on an Alliant FX/8 and on a Sequent Symmetry S81b as well as comparisons with the cyclic reduction algorithm and Gaussian elimination will be presented.
Unable to display preview. Download preview PDF.
- Bondeli S.: A new Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations, Report 130, Departement für Informatik, ETH Zürich 1990.Google Scholar
- Evans D.J.: Parallel Processing, Cambridge University Press, Cambridge 1982.Google Scholar
- Hockney R., Jesshope C.: Parallel Computers, Adam Hilger Ltd., Bristol, 1981.Google Scholar
- Hockney R., Jesshope C.: Parallel Computers 2, Adam Hilger Ltd., Bristol, 1988.Google Scholar
- Lakshmivarahan S., Dhall S.K.: A new class of parallel algorithms for solving linear tridiagonal systems, 1986 315–324.Google Scholar
- Lambiotte J., Voigt R.: The Solution of Tridiagonal Linear Systems on the CDC STAR-100 Computer, ACM Trans. Math. Soft. 1, 308–329.Google Scholar
- Ortega J., Introduction to Parallel and Vector Solution of Linear Systems, Plenum Press, New York 1988.Google Scholar
- Schoenauer W.: Scientific Computing on Vector Computers, North-Holland 1987.Google Scholar