The explicit inverses of general tridiagonal matrices and some applications

A. Cichocki, R. Unbehauen

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Tridiagonal or Jacobi matrices arise in several problems in electrical engineering as well as in different areas of mathematics. - However, there is little known on the inverses of such matrices. The explicit inverses of general tridiagonal matrices are presented in this paper. The method is based on an efficient implementation of Cramer's rule or Coate's flow graph technique and the theory of continuants. The technique is well suited to computer programming and is extremely efficient in symbolical analysis of electrical networks. It could also be efficiently implemented on a parallel computer. - Sensitivity studies or modern optimization techniques used in iterative network synthesis often require the computation of partial derivatives. The proposed technique permits these to be calculated analytically with great case.

Original languageEnglish
Pages (from-to)255-260
Number of pages6
JournalArchiv für Elektrotechnik
Volume69
Issue number4
DOIs
Publication statusPublished - Jul 1986
Externally publishedYes

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