Parallel Exact and Approximate Arrow-Type Inverses on Symmetric Multiprocessor Systems

  • George A. Gravvanis
  • Konstantinos M. Giannoutakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)


In this paper we present new parallel inverse arrow-type matrix algorithms based on the concept of sparse factorization procedures, for computing explicitly exact and approximate inverses, on symmetric multiprocessor systems. The parallel implementation of the new inversion algorithms is discussed and numerical results are presented, using the simulation tool of Multi-Pascal.


Multiprocessor System Relative Speedup Sparse Linear System Approximate Inverse Putational Method 
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.


  1. 1.
    Akl, S.G.: Parallel Computation: Models and Methods. Prentice-Hall, Englewood Cliffs (1997)Google Scholar
  2. 2.
    Dongarra, J.J., Duff, I., Sorensen, D., van der Vorst, H.A.: Numerical Linear Algebra for High-Performance Computers. SIAM, Philadelphia (1998)MATHCrossRefGoogle Scholar
  3. 3.
    Duff, I.: The impact of high performance computing in the solution of linear systems: trends and problems. J. Comp. Applied Math. 123, 515–530 (2000)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Evans, D.J.: Preconditioning Methods: Theory and Applications. Gordon and Breach Science Publishers (1983)Google Scholar
  5. 5.
    Gravvanis, G.A.: Explicit Approximate Inverse Preconditioning Techniques. Archives of Computational Methods in Engineering 9(4), 371–402 (2002)MATHCrossRefGoogle Scholar
  6. 6.
    Gravvanis, G.A.: Explicit isomorphic iterative methods for solving arrow-type linear systems. Inter. J. Comp. Math. 74(2), 195–206 (2000)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gravvanis, G.A.: Solving parabolic and nonlinear 1D problems with periodic boundary conditions. In: CD-ROM Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering 2000 (2000)Google Scholar
  8. 8.
    Gravvanis, G.A.: Parallel preconditioned algorithms for solving special tridiagonal systems. In: Proceedings of Dynamical Systems and Applications III, pp. 241–248. Dynamic Publishers (1999)Google Scholar
  9. 9.
    Gravvanis, G.A.: Parallel matrix techniques. In: Papailiou, K., Tsahalis, D., Periaux, J., Hirsch, C., Pandolfi, M. (eds.) Computational Fluid Dynamics I, pp. 472–477. Wiley, Chichester (1998)Google Scholar
  10. 10.
    Gravvanis, G.A., Platis, A.N., Giannoutakis, K.M., Violentis, J.B., Lipitakis, E.A.: Performability evaluation of multitasking and multiprocessor systems by explicit approximate inverses. In: Arabnia, H.R., Mun, Y. (eds.) Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, pp. 1324–1331. CSREA Press (2003)Google Scholar
  11. 11.
    Grote, M.J., Huckle, T.: Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18, 838–853 (1977)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Grote, M.J., Simon, H.D.: Parallel preconditioning and approximate inverses on the connection machine. In: Sincovec, R.F., Keyes, D.E., Petzold, L.R., Reed, D.A. (eds.) Parallel Processing for Scientific Computing, vol. 2, pp. 519–523. SIAM, Philadelphia (1993)Google Scholar
  13. 13.
    Lester, B.P.: The Art of Parallel Programming. Prentice-Hall Int. Inc., Englewood Cliffs (1993)Google Scholar
  14. 14.
    Saad, Y., van der Vorst, H.A.: Iterative solution of linear systems in the 20th century. J. Comp. Applied Math. 123, 1–33 (2000)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • George A. Gravvanis
    • 1
  • Konstantinos M. Giannoutakis
    • 1
  1. 1.Department of Electrical and Computer Engineering, School of EngineeringDemocritus University of ThraceXanthiGreece

Personalised recommendations