, Volume 56, Issue 4, pp 385–395 | Cite as

A parallel algorithm for solving special tridiagonal systems on ring networks

  • K. -L. Chung
  • W. -M. Yan
  • J. -G. Wu


The solution of special linear, circulant-tridiagonal systems is considered. In this paper, a fast parallel algorithm for solving the special tridiagonal systems, which includes the skew-symmetric and tridiagonal-Toeplitz systems, is presented. Employing the diagonally dominant property, our parallel solver does need only local communications between adjacent processors on a ring network. An error analysis is also given. On the nCUBE/2E multiprocessors, some experimental results demonstrate the good performance of our stable parallel solver.

AMS Subject Classifications

65F05 15A23 

Key words

nCUBE/2E multiprocessors matrix perturbation parallel algorithm performance ring network tridiagonal Toeplitz linear systems 

Ein parelleler Algorithmus zur Lösung spezieller Tridiagonalsysteme auf Ring-Netzwerken


Wir betrachten die Lösung einer Klasse von speziellen tridiagonalen Gleichungssystemen, die schiefsymmetrische und Töplitz-Systeme einschließt, und geben einen schnellen, parallelen, Algorithmus dafür an. Bei Vorliegen von Diagonal-Dominanz benötigt unser paralleler Solver nur Kommunikation zwischen benachbarten Prozessoren auf einem Ring-Netzwerk. Eine Fehleranalyse wird angegeben. Einige experimentelle Resultate, die auf einem nCUBE/2E Gerät gewonnen wurden, zeigen das gute Verhalten unseres stabilen, parallelen Solvers.


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • K. -L. Chung
    • 1
  • W. -M. Yan
    • 2
  • J. -G. Wu
    • 3
  1. 1.Department of Information ManagementNational Taiwan Institute of TechnologyTaipeiTaiwan, R.O.C.
  2. 2.Department of Computer Science and Information EngineeringNational Taiwan UniversityTaipeiTaiwan, R.O.C.
  3. 3.Department of Information and Computer EducationNational Taiwan Normal UniversityTaipeiTaiwan, R.O.C.

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