Geodesic
Transient behavior of powers and exponentials of large Toeplitz matrices
Electronic transactions on numerical analysis, Tome 18 (2004), pp. 1-41.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The message of this paper is that powers of large Toeplitz matrices show critical behavior if and only if the norm of the symbol is greater than one. Critical behavior means that the norms of the powers grow $\textcent $###$\sterling $exponentially to infinity or that they run through a critical transient phase before decaying exponentially to zero. We summarize several known results that are relevant to the problem. Moreover, the paper contains some new results and illuminates the question from a perspective that might be new. The paper may serve as an introduction to a few basic phenomena one encounters in the field.
Classification : 47B35, 15A60, 65F35
Keywords: Toeplitz matrix, matrix power, matrix exponential, transient behavior 
@article{ETNA_2004__18__a12,
     author = {B\"ottcher, Albrecht},
     title = {Transient behavior of powers and exponentials of large {Toeplitz} matrices},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--41},
     publisher = {mathdoc},
     volume = {18},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__18__a12/}
}
TY  - JOUR
AU  - Böttcher, Albrecht
TI  - Transient behavior of powers and exponentials of large Toeplitz matrices
JO  - Electronic transactions on numerical analysis
PY  - 2004
SP  - 1
EP  - 41
VL  - 18
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2004__18__a12/
LA  - en
ID  - ETNA_2004__18__a12
ER  - 
%0 Journal Article
%A Böttcher, Albrecht
%T Transient behavior of powers and exponentials of large Toeplitz matrices
%J Electronic transactions on numerical analysis
%D 2004
%P 1-41
%V 18
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2004__18__a12/
%G en
%F ETNA_2004__18__a12
Böttcher, Albrecht. Transient behavior of powers and exponentials of large Toeplitz matrices. Electronic transactions on numerical analysis, Tome 18 (2004), pp. 1-41. http://geodesic.mathdoc.fr/item/ETNA_2004__18__a12/