Abstract
The partitioning algorithm which is a modification of Wang's method for tridiagonal equations is stabilized to the case of arbitrary well conditioned matrix. A realization on Parallel Virtual Machine (PVM) is presented. The parallel solution is analysed under different loads: system dimension, variable numbers of virtual machines and different kind of bandwidth local area networks.
This work supported in part by Grant MM-434/94 from the National Scientific Research Fund of the Bulgarian Ministry of Education and Science.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Amodio, P., Brugnano, L., Politi, T.: Parallel Factorizations for tridiagonal matrices. SIAM J. Numer. Anal. 30 (1993) 813–823
Amodio, P., Mazzia, F.: Backward error analysis of cyclic reduction for the solution of tridiagonal systems. Mathematics of Computation 62 (1994) 601–617
Amodio, P., Trigiante, D.: A parallel direct method for solving initial value problems for ordinary differential equations. Applied Numerical Mathematics 11 (1993) 85–93
Balle, S., Hansen, P., Higham, N.: A Strassen-Type Matrix Inversion Algorithm for the Connection Machine. APPARC PaA2 Deliverable, Esprit BRA Contract # 6634; Report UNIC-93-11, UNI•C (1993)
Dongarra, J., Sameh, A.: On some parallel banded system solvers. Parallel Computing 1 (1984) 223–235
Geist, A., Beguelin, A., Dongarra, J., Jiang, W., Manchenk, R., Sunderam, V.: PVM: Parallel Virtual Machine. A Users' Guide and Tutorial for Networked Parallel Computing. The MIT Press (1994)
Higham, D., Higham, N.: Backward error and condition of structured linear systems. SIAM J. Matrix Anal. Appl. 13 (1992) 162–175
Golub, G., Van Loan, C.: Matrix Computations. The John Hopkins University Press (1989)
Hansen, P., Yalamov, P.: Stabilization by Perturbation of a 4n2 Toeplitz Solver. Preprint N25, Technical University of Rousse (1995)
Stone, H.: An efficient parallel algorithm for the solution of a tridiagonal linear system of equations. J. Assoc. Comput. Mach. 20 (1973) 27–38
Stone, H.: Parallel tridiagonal solvers. ACM Trans. Math. Software 1 (1975) 289–307
Van Der Vorst, H.: Large tridiagonal and block tridiagonal linear systems on vector and parallel computers. Parallel Comput. 5 (1987) 45–54
Wang, H.: A parallel method for tridiagonal equations. ACM Trans. Math. Software 7 (1981) 303–311
Yalamov, P.: On the Stability of the Cyclic Reduction without Back Substitution for Tridiagonal Systems. BIT 34 (1994) 428–447
Yalamov, P.: Stability of a partitioning algorithm for bidiagonal systems. (submitted to SIAM J. Matrix Anal. Appl.)
Yalamov, P.: Convergence of the Iterative Refinement Procedure Applied to Stabilization of a Fast Toeplitz Solver. Preprint N26, Technical University of Rousse (1995)
Yalamov, P., Pavlov, V.: Stability of the Block Cyclic Reduction. Linear Algebra and Its Applications (to appear)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pavlov, V., Todorova, D. (1997). Stabilization and experience with the partitioning method for tridiagonal systems. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_117
Download citation
DOI: https://doi.org/10.1007/3-540-62598-4_117
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62598-8
Online ISBN: 978-3-540-68326-1
eBook Packages: Springer Book Archive