### 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) |
---|---|

Pages (from-to) | 27-33 |

Number of pages | 7 |

Journal | Electric Power Systems Research |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - 1993 |

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### Keywords

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

### ASJC Scopus subject areas

- Energy Engineering and Power Technology
- Electrical and Electronic Engineering

### Cite this

*Electric Power Systems Research*,

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

**Precedence relationship minimization in numerically asymmetric matrix inverse factor calculations.** / Tylavsky, Daniel; Ranganath, J.; Shyam, N.; Chen, S. X.

Research output: Contribution to journal › Article

*Electric Power Systems Research*, vol. 28, no. 1, pp. 27-33. https://doi.org/10.1016/0378-7796(93)90076-Q

}

TY - JOUR

T1 - Precedence relationship minimization in numerically asymmetric matrix inverse factor calculations

AU - Tylavsky, Daniel

AU - Ranganath, J.

AU - Shyam, N.

AU - Chen, S. X.

PY - 1993

Y1 - 1993

N2 - 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 AE, 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.

AB - 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 AE, 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.

KW - Elementary task

KW - Extended matrix

KW - Factorization path

KW - Parallel factorization

KW - Precedence relationships

UR - http://www.scopus.com/inward/record.url?scp=43949166248&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43949166248&partnerID=8YFLogxK

U2 - 10.1016/0378-7796(93)90076-Q

DO - 10.1016/0378-7796(93)90076-Q

M3 - Article

AN - SCOPUS:43949166248

VL - 28

SP - 27

EP - 33

JO - Electric Power Systems Research

JF - Electric Power Systems Research

SN - 0378-7796

IS - 1

ER -