Precedence relationship minimization in numerically asymmetric matrix inverse factor calculations

Daniel Tylavsky, J. Ranganath, N. Shyam, S. X. Chen

Research output: Contribution to journalArticle

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 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.

Original languageEnglish (US)
Pages (from-to)27-33
Number of pages7
JournalElectric Power Systems Research
Volume28
Issue number1
DOIs
StatePublished - 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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