A Parallel Algorithm for Solving Sparse Triangular Systems

Chin Wen Ho, R. C.T. Lee

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, we propose a fast parallel algorithm, which is generalized from the parallel algorithms for solving banded linear systems, to solve sparse triangular systems. We transform the original problem into a directed graph. The solving procedure then consists of eliminating edges in this graph. The worst case time-complexity of this parallel algorithm is O(log2n) where n is the size of the coefficient matrix. When the coefficient matrix is a triangular banded matrix with bandwidth m, then the time-complexity of our algorithm is O(log(m) log(n)).

Original languageEnglish
Pages (from-to)848-852
Number of pages5
JournalIEEE Transactions on Computers
Issue number6
StatePublished - Jun 1990


  • cyclic reduction
  • directed graph model
  • parallel computation
  • presubstitution
  • recursive doubling
  • sparse triangular linear systems


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