# Discrete Mathematics & Theoretical Computer Science

## Volume 5 n° 1 (2002), pp. 109-120

author: | Clémentin Tayou Djamegni |
---|---|

title: | Synthesis Of Space-Time Optimal Systolic Algorithms For The Cholesky Factorization |

keywords: | parallel processing, projection methods, timing function, allocation function, space-time complexity, re-indexation |

abstract: | In this paper we study the synthesis of space-time optimal
systolic arrays for the Cholesky Factorization (CF). First, we discuss
previous allocation methods and their application to CF. Second, stemming from
a new allocation method we
derive a space-time optimal array, with nearest neighbor
connections, that requires 3N + Θ(1) time steps and N^{2}/8 + Θ(N)
processors, where N is the size of the problem. The number of processors
required by this new design improves the best previously known bound,
N^{2}/6 + Θ(N), induced by previous allocation methods.
This is the first contribution of the paper.
The second contribution stemms from the fact that the paper also introduces
a new allocation method that suggests to first perform
index transformations on the initial dependence graph of a given system of
uniform recurrent equations before
applying the weakest allocation method, the projection method.
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

reference: | Clémentin Tayou Djamegni (2002),
Synthesis Of Space-Time Optimal Systolic Algorithms For The Cholesky Factorization,
Discrete Mathematics and Theoretical Computer Science 5, pp. 109-120 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

ps.gz-source: | dm050107.ps.gz (53 K) |

ps-source: | dm050107.ps (186 K) |

pdf-source: | dm050107.pdf (135 K) |

The first *source* gives you the `gzipped' PostScript, the second the plain
PostScript and the third the format for the Adobe accrobat
reader. Depending on the installation of your web browser, at least
one of these should (after some amount of time) pop up a window for
you that shows the full article. If this is not the case, you should
contact your system administrator to install your browser correctly.

Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.

Automatically produced on Fri May 3 21:39:46 CEST 2002 by ifalk