Premium
Computation and presentation of graphs displaying closure hierarchies of Jordan and Kronecker structures
Author(s) -
Elmroth Erik,
Johansson Pedher,
Kågström Bo
Publication year - 2001
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.253
Subject(s) - hierarchy , kronecker product , kronecker delta , closure (psychology) , computation , mathematics , theoretical computer science , graph , matrix (chemical analysis) , computer science , algebra over a field , algorithm , pure mathematics , physics , materials science , quantum mechanics , economics , market economy , composite material
StratiGraph, a Java‐based tool for computation and presentation of closure hierarchies of Jordan and Kronecker structures is presented. The tool is based on recent theoretical results on stratifications of orbits and bundles of matrices and matrix pencils. A stratification reveals the complete hierarchy of nearby structures, information critical for explaining the qualitative behaviour of linear systems under perturbations. StratiGraph facilitates the application of these theories and visualizes the resulting hierarchy as a graph. Nodes in the graph represent orbits or bundles of matrices or matrix pencils. Edges represent covering relations in the closure hierarchy. Given a Jordan or Kronecker structure, a user can obtain the complete information of nearby structures simply by mouse clicks on nodes of interest. This contribution gives an overview of the StratiGraph tool, presents its main functionalities and other features, and illustrates its use by sample applications. Copyright © 2001 John Wiley & Sons, Ltd.