## Abstract

Working within the LogP model, we present parallel triangular solvers which use forward/backward substitution and show that they are optimal. We begin by deriving several lower bounds on execution time for solving triangular linear systems. Specifically, we derive lower bounds in which it is assumed that the number of data items per processor is bounded, a general lower bound, and lower bounds for specific data layouts commonly used for this problem. Furthermore, algorithms are provided which have running times within a constant factor of the lower bounds described. One interesting result is that the popular 2-dimensional block matrix layout necessarily results in significantly longer running times than simpler one-dimensional schemes. Finally, we present a generalization of the lower bounds to banded triangular linear systems.

Original language | English (US) |
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Pages (from-to) | 553-560 |

Number of pages | 8 |

Journal | IEEE Symposium on Parallel and Distributed Processing - Proceedings |

State | Published - 1995 |

Externally published | Yes |

Event | Proceedings of the 1995 7th IEEE Symposium on Parallel and Distributed Processing - San Antonio, TX, USA Duration: Oct 25 1995 → Oct 28 1995 |

## ASJC Scopus subject areas

- General Engineering