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<p>A fast parallel algorithm, which is generalized from the parallel algorithms for solving banded linear systems, is proposed to solve sparse triangular systems. The original problem is transformed 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(log/sup 2/n) 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 the algorithm is O(log(m)*log(n)).</p>
parallel algorithm; sparse triangular systems; banded linear systems; directed graph; worst-case time-complexity; coefficient matrix; triangular banded matrix; computational complexity; directed graphs; parallel algorithms.
R.C.T. Lee, C.-W. Ho, "A Parallel Algorithm for Solving Sparse Triangular Systems", IEEE Transactions on Computers, vol. 39, no. , pp. 848-852, June 1990, doi:10.1109/12.53610
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