Selçuk Journal
of
Applied Mathematics
WinterSpring,
2002
Volume 3
Number 1
Research Center
of
Applied Mathematics

SJAM
WinterSpring 2002, Volume 3  Number 1

Resolvent of matrix polynomials, pseudospectra and inversion
problems 
Jan Kozánek^{*}

Institute of
Thermomechanics, Academy of Sciences of the Czech Republic,
Dolejskova 5, 182 00 Prague 8, Czech Republic.
email:
kozanek@it.cas.cz
Received: March 22, 2002

Summary
This paper deals with the mathematical
model of a dynamic systems written by the n ordinary differential
equations of order m with constant coefficients. The formulas for
the resolvent of matrix polynomial (lmatrix
problem) and for "derivative resolvents", as well theirs derivations
with respect to
l
are given with help of less commonly used linearization form. The
extension of Pseudospectra definition for above matrix polynomial
problem is proposed. The inversion problem, formulated here for
general complex and real coefficient matrices is important in
numerical simulation. As a motivation of the study of an evolutive
dynamic system depending on a one parameter, the famous Lancaster's
example, where m=2 and n=4, is given. 

Key
words
dynamic systems, regular matrix
polynomial problem, linearization, eigenvalue, eigenvector, latent
roots, latent vector, generalized latent vector, Jordan canonical
form, resolvent, state space, component matrices, pseudospectra,
inversion problem

Mathematics Subject
Classification (1991): 34A30, 47A10,
15A18, 15A22, 34A55
*
This research was supported by the Grant Agency of the Czech
Republic (No 101/00/1471).

Article in PS format (314 Kb) 
Article in ZIP format (113 Kb) 
