A distributed memory parallel Gauss-Seidel algorithm for linear algebraic systems

  • Authors:

  • Yueqiang Shang

  • Affiliations:

  • Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, PR China and School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, PR China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2009

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Abstract

A distributed memory parallel Gauss-Seidel algorithm for linear algebraic systems is presented, in which a parameter is introduced to adapt the algorithm to different distributed memory parallel architectures. In this algorithm, the coefficient matrix and the right-hand side of the linear algebraic system are first divided into row-blocks in the natural rowwise-order according to the performance of the parallel architecture in use. And then these row-blocks are distributed among local memories of all processors through torus-wrap mapping techniques. The solution iteration vector is cyclically conveyed among processors at each iteration so as to decrease the communication. The algorithm is a true Gauss-Seidel algorithm which maintains the convergence rate of the serial Gauss-Seidel algorithm and allows existing sequential codes to run in a parallel environment with a little investment in recoding. Numerical results are also given which show that the algorithm is of relatively high efficiency.