Abstract
In this paper we present a new efficient algorithm for solving linear recurrence systems with constant coefficients on distributed memory machines and clusters of workstations. The algorithm is based on level 3 and level 1 BLAS (Basic Linear Algebra Subprograms) routines _GEMM and _AXPY. We also discuss its platform-independent implementation with BLACS (Basic Linear Algebra Communication Subprograms) and finally present the results of experiments performed on a cluster of Pentium II computers running under Linux with operating system with MPI (Message-Passing Interface) and compare the results with the performance of a simple divide-and-conquer algorithm proposed in our earlier work.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dongarra, J., Duff, I., Sorensen, D., Van der Vorst, H.: Solving Linear Systems on Vector and Shared Memory Computers. SIAM, Philadelphia (1991)
Dongarra, J. J., Whaley, R. C.: LAPACK Working Note 94: A User’s Guide to the BLACS v1.1, http://www.netlib.org/lapack/lawns
Geist, A., Beguelin, A., Dongarra, J., Jiang, W., Manchek, R., Sunderam, V.: PVM: A Users’ Guide and Tutorial for Networked Parallel Computing. MIT Press (1994)
Gropp, W., Lusk, E.: User’s Guide for mpich, a Portable Implementation of MPI Version 1.2.0, ftp://ftp.mcs.anl.gov/pub/mpi/userguide.ps
Modi, J.: Parallel Algorithms and Matrix Computations. Oxford University Press, Oxford (1988)
Paprzycki, M., Stpiczyński, P.: Solving linear recurrence systems on parallel computers. In: Proceedings of the Mardi Gras’ 94 Conference, Baton Rouge, Feb. 10–12, 1994. Nova Science Publishers, New York (1995) 379–384
P. Pacheco: Parallel Programming with MPI. Morgan Kaufmann, San Francisco (1996)
M. Paprzycki and P. Stpiczyński: Parallel solution of linear recurrence systems. Z. Angew. Math. Mech. 76(1996), Suppl. 2, 5–8
Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. 2nd edn. Springer, New York (1993)
Stpiczyński, P.: Parallel algorithms for solving linear recurrence systems. In: L. Bougé et al. (eds.): Lecture Notes in Computer Science, Vol. 634. Springer-Verlag, Berlin (1992) 343–348
Stpiczyński, P.: Efficient data parallel algorithms for computing trigonometric sums. Submitted to Ann. Univ. Mariae Curie-Skłodowska Sect. A
Stpiczyński, P., Paprzycki, M.: Parallel algorithms for finding trigonometric sums, In: D.H. Bailey et al. (eds.): Parallel Processing for Scientific Computing. SIAM, Philadelphia (1995) 291–292
Stpiczyński, P., Paprzycki, M.: Fully Vectorized Solver for Linear Recurrence Systems with Constant Coefficients. In: Proceedings of VECPAR 2000. Facultade de Engerharia do Universidade do Porto, Porto (2000) 541–551
Whaley, R. C.: LAPACK Working Note 73: Basic Linear Communication Algebra Subprograms: Analysis and Implementation Across Multiple Parallel Architectures, http://www.netlib.org/lapack/lawns
Whaley, R. C., Petitet, A., Dongarra, J. J.: Automated empirical optimizations of software and the ATLAS project. Parallel Comput. 27 (2001) 3–35
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stpiczyński, P. (2002). A New Message Passing Algorithm for Solving Linear Recurrence Systems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_51
Download citation
DOI: https://doi.org/10.1007/3-540-48086-2_51
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43792-5
Online ISBN: 978-3-540-48086-0
eBook Packages: Springer Book Archive