Abstract
A fast and efficient parallel algorithm for tridiagonal matrix inversion is presented. The algorithm is based on partitioning and reordering the initial tridiagonal matrix which allows us to parallelize it efficiently. The algorithm is implemented on a linear processor array. For interprocessor communication we consider three types of network components: dual-port RAM, FIFO RAM and a router. We derive the performances of the algorithm and the system which relates to the number of calculation steps, speedup and efficiency. The obtained results show that the method is highly valuable.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Faddejev, D.K., Faddejeva, V.N.: Numerical Methods in Linear Algebra. Fizmatigiz, Moscow, 1963 (in Russian).
Francomano, E., Pecorella, A., Tortorici Macaluso, A.: Parallel experience on the inverse matrix computation. Parallel Computing 17 (1991), 907–912.
Swartrauber, P.N., Sweet, R.A.: Vector and Parallel methods for the direct solution of Poisson's equation. Journal of Computational and Applied Mathematics 27 (1989), 241–263.
Hajj, I.N., Skelboe, S.: A Multilevel Parallel Solver for Block Tridiagonal and Banded Linear Systems. Parallel Computing 15 (1990), 21–45.
Hajj, I.N., Skelboe, S.: Multilevel Parallel Solver for Banded Linear Systems. Aspects of Computations on Asynchronous Parallel Processors, M.H. Wright (Ed.) Elsevier Science Publishers B.V. (North-Holland), IFIP 1989, 69–78.
Evans, D.J., Megson, G.M.: Fast Triangularization of a Symmetric Tridiagonal Matrix. Journal of Parallel and Distributed Computing 6 (1989), 663–678.
Reuter, R.: Solving Tridiagonal Systems of Linear Equations on the IBM 3090 VF. Parallel Computing 8 (1988), 331–376.
Bondeli, S.: Divide and Conquer: Parallele Algorithmen zur Lösung tridiagonaler Gleichungsysteme. Informatik-Dissertationen ETH Zürich, Nr.30 (1991).
Van der Vorst, H.A.: Large Tridiagonal and Block Tridiagonal Linear Systems on Vector and Parallel Computers. Parallel Computing 5 (1987), 45–54.
Milovanović, I.Ž., Milovanović, E.I., Stojčev, M.K: Matrix Inversion Algorithm for Linear Array Processor. Math. Comput. Modeling 16 (12)(1992), 133–141.
Ni, L.M., McKinley, P.K.: A Survey of Wormhole Routing Techniques in Direct Networks. Computer, Vol. 26, No. 2(1993), 62–76.
Gaughan, P.T., Yalamanchili, S.: Adaptive Routing Protocols for Hypercube Interconnection Networks. Computer, Vol. 26, No. 5(1993), 12–23.
Zhang, X.: System Effects of Interprocessor Communication Latency in Multicomputers. IEEE Micro, Vol. 11, No. 2(1991), 13–15, 52–55.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stojčev, M.K., Milovanović, E.I., Mihajlović, M.D., Milovanović, I.Ž. (1994). Parallel algorithm for inverting tridiagonal matrix on linear processor array. In: Buchberger, B., Volkert, J. (eds) Parallel Processing: CONPAR 94 — VAPP VI. VAPP CONPAR 1994 1994. Lecture Notes in Computer Science, vol 854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58430-7_21
Download citation
DOI: https://doi.org/10.1007/3-540-58430-7_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58430-8
Online ISBN: 978-3-540-48789-0
eBook Packages: Springer Book Archive