Parallel algorithm for inverting tridiagonal matrix on linear processor array
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.
Unable to display preview. Download preview PDF.
- 1.Faddejev, D.K., Faddejeva, V.N.: Numerical Methods in Linear Algebra. Fizmatigiz, Moscow, 1963 (in Russian).Google Scholar
- 2.Francomano, E., Pecorella, A., Tortorici Macaluso, A.: Parallel experience on the inverse matrix computation. Parallel Computing 17 (1991), 907–912.Google Scholar
- 3.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.Google Scholar
- 4.Hajj, I.N., Skelboe, S.: A Multilevel Parallel Solver for Block Tridiagonal and Banded Linear Systems. Parallel Computing 15 (1990), 21–45.Google Scholar
- 5.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.Google Scholar
- 6.Evans, D.J., Megson, G.M.: Fast Triangularization of a Symmetric Tridiagonal Matrix. Journal of Parallel and Distributed Computing 6 (1989), 663–678.Google Scholar
- 7.Reuter, R.: Solving Tridiagonal Systems of Linear Equations on the IBM 3090 VF. Parallel Computing 8 (1988), 331–376.Google Scholar
- 8.Bondeli, S.: Divide and Conquer: Parallele Algorithmen zur Lösung tridiagonaler Gleichungsysteme. Informatik-Dissertationen ETH Zürich, Nr.30 (1991).Google Scholar
- 9.Van der Vorst, H.A.: Large Tridiagonal and Block Tridiagonal Linear Systems on Vector and Parallel Computers. Parallel Computing 5 (1987), 45–54.Google Scholar
- 10.Milovanović, I.Ž., Milovanović, E.I., Stojčev, M.K: Matrix Inversion Algorithm for Linear Array Processor. Math. Comput. Modeling 16 (12)(1992), 133–141.Google Scholar
- 11.Ni, L.M., McKinley, P.K.: A Survey of Wormhole Routing Techniques in Direct Networks. Computer, Vol. 26, No. 2(1993), 62–76.Google Scholar
- 12.Gaughan, P.T., Yalamanchili, S.: Adaptive Routing Protocols for Hypercube Interconnection Networks. Computer, Vol. 26, No. 5(1993), 12–23.Google Scholar
- 13.Zhang, X.: System Effects of Interprocessor Communication Latency in Multicomputers. IEEE Micro, Vol. 11, No. 2(1991), 13–15, 52–55.Google Scholar