HPCN-Europe 1997: High-Performance Computing and Networking pp 319-331 | Cite as
A two-way BSP algorithm for tridiagonal systems
Conference paper
First Online:
Abstract
A two-way parallel recursive method is presented for solving a tridiagonal linear system. The algorithm is based on the parallel segment recursive method proposed in [9]. The computation and communication costs of the algorithm are analysed using the BSP (Bulk Synchronous Parallel) model.
Keywords
Parallel Machine Grand Unify Theory Linear Recurrence Cyclic Reduction Tridiagonal System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.R.H. Bisseling and W.F. McColl, Scientific computing on bulk synchronous parallel architectures, Technical Report No. 836., Department of Mathematics, University of Utrecht”, Dec. 1993.Google Scholar
- 2.E. Dekker and L. Dekker, Parallel minimal norm method for tridiagonal linear systems, IEEE Trans. Computers., vol. 44, no. 7, pp. 942–946, 1995.Google Scholar
- 3.P. Dubois and G. Rodrigue, An analysis of the recursive doubling algorithm, in High Speed Computer and Algorithm Organization., Kuck et al., Eds. New York, Academic, 1977.Google Scholar
- 4.Ö. Eğecioğlu, C.K. Koc and A.J. Laub, A recursive doubling algorithm for solution of tridiagonal systems on hypercube multiprocessors, J. Computat. Appl. Math., vol. 27, pp. 95–108, 1989.Google Scholar
- 5.G.H. Golub and C.F. Van Loan, Matrix Computations., Johns Hopkins University Press, Baltimore, MD, 1983.Google Scholar
- 6.J.M.D. Hill, P.I. Crumpton and D.A. Burgess, The theory, practice, and a tool for BSP performance prediction applied to a CFD application, Technical Report, No. 96/03 Oxford University Computing Lab. February, 1996.Google Scholar
- 7.R.W. Hockney, A fast direct solution of poisson's equation using Fourier analysis, J. ACM., 12 (1), pp. 95–113, 1965.Google Scholar
- 8.R.W. Hockney and C.R. Jesshope, Parallel Computers 2., Philadelphia, PA, Adam Hilger, 1988.Google Scholar
- 9.Y. Huang, Parallel recursive method for tridiagonal systems, Procs. 1997 Advances in Parallel and Distributed Computing., IEEE CS Press, March 19–21, 1997.Google Scholar
- 10.Y. Huang and W.F. McColl, Generalised Tridiagonal Matrix Inversion, 15th IMACS World Congress on Scientific Computation, Modeling and Applied Mathematics., Berlin, Aug 24–29, 1997. To appear.Google Scholar
- 11.P.M. Kogge and H.S. Stone, A parallel algorithm for efficient solution of a general class of recurrence equations, IEEE Trans. Computers., vol. 22, no. 8, pp.786–793, 1973.Google Scholar
- 12.W.F. McColl, Scalable parallel computing: A grand unified theory and its practical development, Procs. 13th IFIP World Computer Congress. (B. Pehrson and I.Simon, eds.), Vol. 1 (Invited Paper), Elsevier, pp. 539–546, 1994.Google Scholar
- 13.W.F. McColl, BSP Programming, in Specification of Parallel Algorithms. (G.E. Blelloch, K.M. Chandy and S. Jagannathan eds.), Procs. DIMACS Workshop, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 18, pp. 21–35, 1994.Google Scholar
- 14.W.F. McColl, Scalable Computing, in Computer Science Today: Recent Trends and Developments. (J. Van Leeuwen ed.), LNCS Volume 1000, Springer-Verlag, pp. 46–61, 1995.Google Scholar
- 15.H.S. Stone, An efficient parallel algorithm for the solution of a tridiagonal linear system of equations, J. Assoc. Compu. Mach., 20 (1), pp. 27–38, 1973.Google Scholar
- 16.H.S. Stone, Parallel tridiagonal equation solvers, ACM Trans. Math. Software., 1 (4), pp. 289–307, 1975.Google Scholar
- 17.H.A. Van der Vorst, Large tridiagonal and block tridiagonal linear systems on vector and parallel computers, Parallel Computing., 5, pp. 45–54, 1987.Google Scholar
- 18.L. Valiant, A bridging model for parallel computation, Communications of the ACM., vol. 33, no. 8, Aug. 1990.Google Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 1997