An algorithm for computing minimal Geršgorin sets

Vladimir R. Kostić, Agnieszka K Miedlar, Ljiljana Cvetković

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Summary: The existing algorithms for computing the minimal Geršgorin set are designed for small and medium size (irreducible) matrices and based on Perron root computations coupled with bisection method and sampling techniques. Here, we first discuss the drawbacks of the existing methods and present a new approach based on the modified Newton's method to find zeros of the parameter dependent left-most eigenvalue of a Z-matrix and a special curve tracing procedure. The advantages of the new approach are presented on several test examples that arise in practical applications. Copyright

Original languageEnglish (US)
Pages (from-to)272-290
Number of pages19
JournalNumerical Linear Algebra with Applications
Volume23
Issue number2
DOIs
StatePublished - Mar 1 2016

Keywords

  • Curve tracing
  • Eigenvalue localization
  • Minimal Geršgorin set

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