Premium
Dynamical analysis of numerical systems
Author(s) -
Batterson Steve
Publication year - 1995
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.1680020310
Subject(s) - convergence (economics) , mathematics , dynamical systems theory , numerical analysis , schur decomposition , schur complement , algebra over a field , pure mathematics , eigenvalues and eigenvectors , mathematical analysis , physics , quantum mechanics , economics , economic growth
For many years techniques from numerical analysis have been applied fruitfully to the study of dynamical systems. In this paper it is shown that the theory of dynamical systems may be applied to certain computational problems. In particular the question of global convergence of various QR algorithms can be reduced to the study of certain vector iterations derived from Schur forms of matrices. The technique is illustrated in determining the convergence behavior of normal Hessenberg matrices under the Francis and multishift QR iterations.