### Abstract

A parallel algorithm for obtaining the inverse of the U triangular force of a non-numerically symmetric matrix A of dimension n × n is presented in this paper. The method proposed eliminates the precedence relationships involved with the backward substitution process, which is conventionally used to obtain the U^{-1} factors. The inverse factors are obtained by performing the factorization on an extended matrix A_{E}, which is of dimension 2n × 2n. The method exploits the inherent parallelism in calculating the inverse factors during the forward sweep of the factorization process. Thus, a parallel factorization routine can be easily modified to calculate U^{-1} in parallel. Unlike traditional methods involving precedence relations, which require 2p sequential steps (where p is the length of the longest factor path), the proposed method involves only p + 1 precedence relationships.

Original language | English (US) |
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Pages (from-to) | 27-33 |

Number of pages | 7 |

Journal | Electric Power Systems Research |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1993 |

### Keywords

- Elementary task
- Extended matrix
- Factorization path
- Parallel factorization
- Precedence relationships

### ASJC Scopus subject areas

- Energy Engineering and Power Technology
- Electrical and Electronic Engineering

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## Cite this

*Electric Power Systems Research*,

*28*(1), 27-33. https://doi.org/10.1016/0378-7796(93)90076-Q