Parallel solution of sparse linear systems

  • John R. Gilbert
  • Hjálmtýr Hafsteinsson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 318)


Consider a system of linear equations Ax=b, where A is a symmetric positive definite matrix with arbitrary nonzero structure. We present an efficient CREW parallel algorithm to solve such a system by Cholesky factorization with M* processors, where m* is the number of nonzeros in the Cholesky factor of A. The algorithm has two stages. First is a graph-theoretic structure prediction phase, which runs in time O(log2n). There follows a numerical computation phase, which runs in time proportional to the height of the elimination tree of A times a log factor.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • John R. Gilbert
    • 1
    • 2
    • 3
  • Hjálmtýr Hafsteinsson
    • 4
  1. 1.Dept. of Science and TechnologyChristian Michelsen InstituteFantoft, BergenNorway
  2. 2.University of BergenNorway
  3. 3.Cornell UniversityUSA
  4. 4.Computer Science DepartmentCornell UniversityIthacaUSA

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