Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO

  • Olaf Schenk
  • Klaus Gärtner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2330)


Supernode pivoting for unsymmetric matrices coupled with supernode partitioning and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and prepermutation of rows is used to place large matrix entries on the diagonal. Supernode pivoting allows dynamical interchanges of columns and rows during the factorization process. The BLAS-3 level efficiency is retained. An enhanced left—right looking scheduling scheme is uneffected and results in good speedup on SMP machines without increasing the operation count. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.


Sparse Matrice Sparse Linear System Operation Count Partial Pivoting Nest Dissection 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Olaf Schenk
    • 1
  • Klaus Gärtner
    • 2
  1. 1.Department of Computer ScienceUniversity of BaselBaselSwitzerland
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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